Algebra Books

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Book SynopsisTable of Contents1. Linear Functions, Equations, and Inequalities 1.1 Real Numbers and the Rectangular Coordinate System 1.2 Introduction to Relations and Functions Reviewing Basic Concepts (Sections 1.1 - 1.2) 1.3 Linear Functions 1.4 Equations of Lines and Linear Models Reviewing Basic Concepts (Sections 1.3 - 1.4) 1.5 Linear Equations and Inequalities Unifying Linear Functions 1.6 Applications of Linear Functions Reviewing Basic Concepts (Sections 1.5 - 1.6) Summary Review Exercises Test 2. Analysis of Graphs of Functions 2.1 Graphs of Basic Functions and Relations; Symmetry 2.2 Vertical and Horizontal Shifts of Graphs 2.3 Stretching, Shrinking, and Reflecting Graphs Reviewing Basic Concepts (Sections 2.1 - 2.3) 2.4 Absolute Value Functions Unifying Absolute Value Functions 2.5 Piecewise-Defined Functions 2.6 Operations and Composition Reviewing Basic Concepts (Sections 2.4 - 2.6) Summary Review Exercises Test 3. Quadratic Functions 3.1 Complex Numbers 3.2 Quadratic Functions and Graphs Reviewing Basic Concepts (Sections 3.1 - 3.2) 3.3 Quadratic Equations and Inequalities Unifying Quadratic Functions 3.4 Applications of Quadratic Functions and Models Reviewing Basic Concepts (Sections 3.3 - 3.4) Summary Review Exercises Test 4. Polynomial Functions of Higher Degree 4.1 Graphs of Polynomial Functions 4.2 Topics in the Theory of Polynomial Functions (I) Reviewing Basic Concepts (Sections 4.1 - 4.2) 4.3 Topics in the Theory of Polynomial Functions (II) 4.4 Polynomial Equations, Inequalities, Applications, and Models Reviewing Basic Concepts (Sections 4.3 - 4.4) Unifying Polynomial Functions Summary Review Exercises Test 5. Rational, Power, and Root Functions 5.1 Rational Functions and Graphs (I) 5.2 Rational Functions and Graphs (II) 5.3 Rational Equations, Inequalities, Models, and Applications Reviewing Basic Concepts (Sections 5.1 - 5.3) 5.4 Functions Defined by Powers and Roots 5.5 Equations, Inequalities, and Applications Involving Root Functions Reviewing Basic Concepts (Sections 5.4 - 5.5) Unifying Root Functions Summary Review Exercises Test 6. Inverse, Exponential, and Logarithmic Functions 6.1 Inverse Functions 6.2 Exponential Functions Unifying Exponential Functions 6.3 Logarithms and Their Properties Reviewing Basic Concepts (Sections 6.1 - 6.3) 6.4 Logarithmic Functions 6.5 Exponential and Logarithmic Equations and Inequalities Unifying Logarithmic Functions 6.6 Further Applications and Modeling with Exponential and Logarithmic Functions Reviewing Basic Concepts (Sections 6.4 - 6.6) Summary Exercises on Functions: Domains, Defining Equations, and Composition Summary Review Exercises Test 7. Systems and Matrices 7.1 Systems of Equations 7.2 Solution of Linear Systems in Three Variables 7.3 Solution of Linear Systems by Row Transformations Reviewing Basic Concepts (Sections 7.1 - 7.3) 7.4 Matrix Properties and Operations 7.5 Determinants and Cramer's Rule 7.6 Solution of Linear Systems by Matrix Inverses Reviewing Basic Concepts (Sections 7.4 - 7.6) 7.7 Systems of Inequalities and Linear Programming 7.8 Partial Fractions Reviewing Basic Concepts (Sections 7.7 - 7.8) Summary Review Exercises Test 8. Conic Sections, Nonlinear Systems, and Parametric Equations 8.1 Circles Revisited and Parabolas 8.2 Ellipses and Hyperbolas Reviewing Basic Concepts (Sections 8.1 - 8.2) 8.3 The Conic Sections and Nonlinear Systems 8.4 Introduction to Parametric Equations Reviewing Basic Concepts (Sections 8.3 - 8.4) Summary Review Exercises Test 9. Trigonometric Functions and Applications 9.1 Angles, Arcs, and Their Measures 9.2 Trigonometric Functions and Fundamental Identities 9.3 Right Triangles and Evaluating Trigonometric Functions 9.4 Applications of Right Triangles 9.5 The Circular Functions 9.6 Graphs of the Sine and Cosine Functions 9.7 Graphs of the Other Circular Functions 9.8 Harmonic Motion Summary Review Exercises Test 10. Trigonometric Identities and Equations 10.1 Trigonometric Identities 10.2 Sum and Difference Identities 10.3 Further Identities 10.4 The Inverse Circular Functions 10.5 Trigonometric Equations and Inequalities (I) 10.6 Trigonometric Equations and Inequalities (II) Unifying Trigonometric Functions Summary Review Exercises Test 11. Applications of Trigonometry and Vectors 11.1 The Law of Sines 11.2 The Law of Cosines and Area Formulas 11.3 Vectors and Their Applications 11.4 Trigonometric (Polar) Form of Complex Numbers 11.5 Powers and Roots of Complex Numbers 11.6 Polar Equations and Graphs 11.7 More Parametric Equations Summary Review Exercises Test 12. Further Topics in Algebra 12.1 Sequences and Series 12.2 Arithmetic Sequences and Series 12.3 Geometric Sequences and Series Reviewing Basic Concepts (Sections 12.1 - 12.3) 12.4 Counting Theory 12.5 The Binomial Theorem Reviewing Basic Concepts (Sections 12.4 -12.5) 12.6 Mathematical Induction 12.7 Probability Reviewing Basic Concepts (Sections 12.6 - 12.7) Summary Review Exercises Test R. Review: Basic Algebraic Concepts R.1 Review of Sets R.2 Review of Exponents and Polynomials R.3 Review of Factoring R.4 Review of Rational Expressions R.5 Review of Negative and Rational Exponents R.6 Review of Radicals Test Appendices A: Geometry Formulas B: Vectors in Space C: Polar Form of Conic Sections D: Rotation of Axes Instructor's Answers Answers to Selected Exercises (Note: In the AIE, Instructor's Answers replaces Answers to Selected Exercises.) Index

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Book SynopsisAbout our author Elayn Martin-Gay has taught mathematics at the University of New Orleans for more than 25 years. Her numerous teaching awards include the local University Alumni Association's Award for Excellence in Teaching, and Outstanding Developmental Educator at University of New Orleans, presented by the Louisiana Association of Developmental Educators. Prior to writing textbooks, Elayn Martin-Gay developed an acclaimed series of lecture videos to support developmental mathematics students. These highly successful videos originally served as the foundation materials for her texts. Today, the videos are specific to each book in her series. She has also created Chapter Test Prep Videos to help students during their most teachable moment (as they prepare for a test) along with Instructor-to-Instructor videos that provide teaching tips, hints, and suggestions for every developmental mathematics course, including basic mathematics,Table of ContentsTable of Contents The Whole Numbers 1.1 Study Skill Tips for Success in Mathematics 1.2 Place Value, Names for Numbers, and Reading Tables 1.3 Adding and Subtracting Whole Numbers, and Perimeter 1.4 Rounding and Estimating 1.5 Multiplying Whole Numbers and Area 1.6 Dividing Whole Numbers Integrated Review–Operations on Whole Numbers 1.7 Exponents and Order of Operations 1.8 Introduction to Variables, Algebraic Expressions, and Equations Integers and Introduction to Solving Equations 2.1 Introduction to Integers 2.2 Adding Integers 2.3 Subtracting Integers 2.4 Multiplying and Dividing Integers Integrated Review–Integers 2.5 Order of Operations 2.6 Solving Equations: The Addition and Multiplication Properties Solving Equations and Problem Solving 3.1 Simplifying Algebraic Expressions 3.2 Solving Equations: Review of the Addition and Multiplication Properties Integrated Review–Expressions and Equations 3.3 Solving Linear Equations in One Variable 3.4 Linear Equations in One Variable and Problem Solving Fractions and Mixed Numbers 4.1 Introduction to Fractions and Mixed Numbers 4.2 Factors and Simplest Form 4.3 Multiplying and Dividing Fractions 4.4 Adding and Subtracting Like Fractions, Least Common Denominator, and Equivalent Fractions 4.5 Adding and Subtracting Unlike Fractions Integrated Review–Summary on Fractions and Operations on Fractions 4.6 Complex Fractions and Review of Order of Operations 4.7 Operations on Mixed Numbers 4.8 Solving Equations Containing Fractions Decimals 5.1 Introduction to Decimals 5.2 Adding and Subtracting Decimals 5.3 Multiplying Decimals and Circumference of a Circle 5.4 Dividing Decimals Integrated Review–Operations on Decimals 5.5 Fractions, Decimals, and Order of Operations 5.6 Solving Equations Containing Decimals 5.7 Decimal Applications: Mean, Median, and Mode Ratio, Proportion, and Percent 6.1 Ratio and Proportion 6.2 Percents, Decimals, and Fractions 6.3 Solving Percent Problems with Equations 6.4 Solving Percent Problems with Proportions Integrated Review–Ratio, Proportion, and Percent 6.5 Applications of Percent 6.6 Percent and Problem Solving: Sales Tax, Commission, and Discount 6.7 Percent and Problem Solving: Interest Graphs, Triangle Applications, and Introduction to Statistics and Probability 7.1 Pictographs, Bar Graphs, Histograms, Line Graphs, and Introduction to Statistics 7.2 Circle Graphs Integrated Review–Reading Graphs 7.3 Square Roots and the Pythagorean Theorem 7.4 Congruent and Similar Triangles 7.5 Counting and Introduction to Probability Geometry and Measurement 8.1 Lines and Angles 8.2 Perimeter 8.3 Area, Volume, and Surface Area Integrated Review–Geometry Concepts 8.4 Linear Measurement 8.5 Weight and Mass 8.6 Capacity 8.7 Temperature and Conversions Between the U.S. and Metric Systems Equations, Inequalities, and Problem Solving 9.1 Symbols and Sets of Numbers 9.2 Properties of Real Numbers 9.3 Further Solving Linear Equations Integrated Review–Real Numbers and Solving Linear Equations 9.4 Further Problem Solving 9.5 Formulas and Problem Solving 9.6 Linear Inequalities and Problem Solving Exponents and Polynomials 10.1 Exponents 10.2 Negative Exponents and Scientific Notation 10.3 Introduction to Polynomials 10.4 Adding and Subtracting Polynomials 10.5 Multiplying Polynomials 10.6 Special Products Integrated Review–Exponents and Operations on Polynomials 10.7 Dividing Polynomials Factoring Polynomials 11.1 The Greatest Common Factor and Factoring by Grouping 11.2 Factoring Trinomials of the Form x2+ bx + c 11.3 Factoring Trinomials of the Form ax2+ bx + c 11.4 Factoring Trinomials of the Form ax2+ bx + c by Grouping 11.5 Factoring Perfect Square Trinomials and the Difference of Two Squares Integrated Review–Choosing a Factoring Strategy 11.6 Solving Quadratic Equations by Factoring 11.7 Quadratic Equations and Problem Solving Rational Expressions 12.1 Simplifying Rational Expressions 12.2 Multiplying and Dividing Rational Expressions 12.3 Adding and Subtracting Rational Expressions with the Same Denominator and Least Common Denominator 12.4 Adding and Subtracting Rational Expressions with Different Denominators 12.5 Solving Equations Containing Rational Expressions Integrated Review–Summary on Rational Expressions 12.6 Rational Equations and Problem Solving 12.7 Simplifying Complex Fractions Graphing Equations and Inequalities 13.1 The Rectangular Coordinate System 13.2 Graphing Linear Equations 13.3 Intercepts 13.4 Slope and Rate of Change 13.5 Equations of Lines Integrated Review–Summary on Linear Equations 13.6 Introduction to Functions 13.7 Graphing Linear Inequalities in Two Variables 13.8 Direct and Inverse Variation Systems of Equations 14.1 Solving Systems of Linear Equations by Graphing 14.2 Solving Systems of Linear Equations by Substitution 14.3 Solving Systems of Linear Equations by Addition Integrated Review–Summary on Solving Systems of Equations 14.4 Systems of Linear Equations and Problem Solving Roots and Radicals 15.1 Introduction to Radicals 15.2 Simplifying Radicals 15.3 Adding and Subtracting Radicals 15.4 Multiplying and Dividing Radicals Integrated Review–Simplifying Radicals 15.5 Solving Equations Containing Radicals 15.6 Radical Equations and Problem Solving Quadratic Equations 16.1 Solving Quadratic Equations by the Square Root Property 16.2 Solving Quadratic Equations by Completing the Square 16.3 Solving Quadratic Equations by the Quadratic Formula Integrated Review–Summary on Solving Quadratic Equations 16.4 Graphing Quadratic Equations in Two Variables Appendix A: Tables A.1 Table of Geometric Figures A.2 Table of Percents, Decimals, and Fraction Equivalents A.3 Table on Finding Common Percents of a Number A.4 Table of Squares and Square Roots Appendix B: Factoring Sums and Differences of Cubes Appendix C: Mixture and Uniform Motion Problem Solving Appendix D: Systems of Linear Inequalities Appendix E: Geometric Formulas Student Resources Study Skills Builders Bigger Picture–Study Guide Outline Practice Final Exam

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Book SynopsisElayn Martin-Gay has taught mathematics at the University of New Orleans for more than 25 years. Her numerous teaching awards include the local University Alumni Association's Award for Excellence in Teaching, and Outstanding Developmental Educator at University of New Orleans, presented by the Louisiana Association of Developmental Educators. Prior to writing textbooks, Elayn Martin-Gay developed an acclaimed series of lecture videos to support developmental mathematics students. These highly successful videos originally served as the foundation materials for her texts. Today, the videos are specific to each book in her series. She has also created Chapter Test Prep Videos to help students during their most teachable moment as they prepare for a testalong with Instructor-to-Instructor videos that provide teaching tips, hints, and suggestions for every developmental mathematics course, including basic mathematics, prealgebra, beginning algebTable of ContentsTable of Contents The Whole Numbers 1.1 Study Skill Tips for Success in Mathematics 1.2 Place Value, Names for Numbers, and Reading Tables 1.3 Adding and Subtracting Whole Numbers, and Perimeter 1.4 Rounding and Estimating 1.5 Multiplying Whole Numbers and Area 1.6 Dividing Whole Numbers Integrated Review–Operations on Whole Numbers 1.7 Exponents and Order of Operations 1.8 Introduction to Variables, Algebraic Expressions, and Equations Integers and Introduction to Solving Equations 2.1 Introduction to Integers 2.2 Adding Integers 2.3 Subtracting Integers 2.4 Multiplying and Dividing Integers Integrated Review–Integers 2.5 Order of Operations 2.6 Solving Equations: The Addition and Multiplication Properties Solving Equations and Problem Solving 3.1 Simplifying Algebraic Expressions 3.2 Solving Equations: Review of the Addition and Multiplication Properties Integrated Review–Expressions and Equations 3.3 Solving Linear Equations in One Variable 3.4 Linear Equations in One Variable and Problem Solving Fractions and Mixed Numbers 4.1 Introduction to Fractions and Mixed Numbers 4.2 Factors and Simplest Form 4.3 Multiplying and Dividing Fractions 4.4 Adding and Subtracting Like Fractions, Least Common Denominator, and Equivalent Fractions 4.5 Adding and Subtracting Unlike Fractions Integrated Review–Summary on Fractions and Operations on Fractions 4.6 Complex Fractions and Review of Order of Operations 4.7 Operations on Mixed Numbers 4.8 Solving Equations Containing Fractions Decimals 5.1 Introduction to Decimals 5.2 Adding and Subtracting Decimals 5.3 Multiplying Decimals and Circumference of a Circle 5.4 Dividing Decimals Integrated Review–Operations on Decimals 5.5 Fractions, Decimals, and Order of Operations 5.6 Solving Equations Containing Decimals 5.7 Decimal Applications: Mean, Median, and Mode Ratio, Proportion, and Triangle Applications 6.1 Ratios and Rates 6.2 Proportions Integrated Review–Ratio, Rate, and Proportion 6.3 Proportions and Problem Solving 6.4 Square Roots and the Pythagorean Theorem 6.5 Congruent and Similar Triangles Percent 7.1 Percents, Decimals, and Fractions 7.2 Solving Percent Problems with Equations 7.3 Solving Percent Problems with Proportions Integrated Review–Percent and Percent Problems 7.4 Applications of Percent 7.5 Percent and Problem Solving: Sales Tax, Commission, and Discount 7.6 Percent and Problem Solving: Interest Graphing and Introduction to Statistics and Probability 8.1 Pictographs, Bar Graphs, Histograms, Line Graphs, and Introduction to Statistics 8.2 Circle Graphs 8.3 The Rectangular Coordinate System and Paired Data Integrated Review–Reading Graphs 8.4 Graphing Linear Equations in Two Variables 8.5 Counting and Introduction to Probability Geometry and Measurement 9.1 Lines and Angles 9.2 Perimeter 9.3 Area, Volume, and Surface Area Integrated Review–Geometry Concepts 9.4 Linear Measurement 9.5 Weight and Mass 9.6 Capacity 9.7 Temperature and Conversions Between the U.S. and Metric Systems Exponents and Polynomials 10.1 Adding and Subtracting Polynomials 10.2 Multiplication Properties of Exponents Integrated Review–Operations on Polynomials 10.3 Multiplying Polynomials 10.4 Introduction to Factoring Polynomials Appendix A: Tables A.1 Tables of Geometric Figures A.2 Table of Percents, Decimals, and Fraction Equivalents A.3 Table on Finding Common Percents of a Number A.4 Table of Squares and Square Roots Appendix B: Quotient Rule and Negative Exponents Appendix C: Scientific Notation Appendix D: Geometric Formulas Student Resources Study Skills Builders Bigger Picture–Study Guide Outline Practice Final Exam

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Book SynopsisElayn Martin-Gay has taught mathematics at the University of New Orleans for more than 25 years. Her numerous teaching awards include the local University Alumni Association's Award for Excellence in Teaching, and Outstanding Developmental Educator at University of New Orleans, presented by the Louisiana Association of Developmental Educators. Prior to writing textbooks, Elayn Martin-Gay developed an acclaimed series of lecture videos to support developmental mathematics students. These highly successful videos originally served as the foundation materials for her texts. Today, the videos are specific to each book in her series. She has also created Chapter Test Prep Videos to help students during their most teachable moment as they prepare for a testalong with Instructor-to-Instructor videos that provide teaching tips, hints, and suggestions for every developmental mathematics course, including basic mathematics, prealgebra, beginning algebTable of ContentsTable of Contents The Whole Numbers 1.1 Study Skill Tips for Success in Mathematics 1.2 Place Value, Names for Numbers, and Reading Tables 1.3 Adding and Subtracting Whole Numbers, and Perimeter 1.4 Rounding and Estimating 1.5 Multiplying Whole Numbers and Area 1.6 Dividing Whole Numbers Integrated Review–Operations on Whole Numbers 1.7 Exponents and Order of Operations 1.8 Introduction to Variables, Algebraic Expressions, and Equations Integers and Introduction to Solving Equations 2.1 Introduction to Integers 2.2 Adding Integers 2.3 Subtracting Integers 2.4 Multiplying and Dividing Integers Integrated Review–Integers 2.5 Order of Operations 2.6 Solving Equations: The Addition and Multiplication Properties Solving Equations and Problem Solving 3.1 Simplifying Algebraic Expressions 3.2 Solving Equations: Review of the Addition and Multiplication Properties Integrated Review–Expressions and Equations 3.3 Solving Linear Equations in One Variable 3.4 Linear Equations in One Variable and Problem Solving Fractions and Mixed Numbers 4.1 Introduction to Fractions and Mixed Numbers 4.2 Factors and Simplest Form 4.3 Multiplying and Dividing Fractions 4.4 Adding and Subtracting Like Fractions, Least Common Denominator, and Equivalent Fractions 4.5 Adding and Subtracting Unlike Fractions Integrated Review–Summary on Fractions and Operations on Fractions 4.6 Complex Fractions and Review of Order of Operations 4.7 Operations on Mixed Numbers 4.8 Solving Equations Containing Fractions Decimals 5.1 Introduction to Decimals 5.2 Adding and Subtracting Decimals 5.3 Multiplying Decimals and Circumference of a Circle 5.4 Dividing Decimals Integrated Review–Operations on Decimals 5.5 Fractions, Decimals, and Order of Operations 5.6 Solving Equations Containing Decimals 5.7 Decimal Applications: Mean, Median, and Mode Ratio, Proportion, and Triangle Applications 6.1 Ratios and Rates 6.2 Proportions Integrated Review–Ratio, Rate, and Proportion 6.3 Proportions and Problem Solving 6.4 Square Roots and the Pythagorean Theorem 6.5 Congruent and Similar Triangles Percent 7.1 Percents, Decimals, and Fractions 7.2 Solving Percent Problems with Equations 7.3 Solving Percent Problems with Proportions Integrated Review–Percent and Percent Problems 7.4 Applications of Percent 7.5 Percent and Problem Solving: Sales Tax, Commission, and Discount 7.6 Percent and Problem Solving: Interest Graphing and Introduction to Statistics and Probability 8.1 Pictographs, Bar Graphs, Histograms, Line Graphs, and Introduction to Statistics 8.2 Circle Graphs 8.3 The Rectangular Coordinate System and Paired Data Integrated Review–Reading Graphs 8.4 Graphing Linear Equations in Two Variables 8.5 Counting and Introduction to Probability Geometry and Measurement 9.1 Lines and Angles 9.2 Perimeter 9.3 Area, Volume, and Surface Area Integrated Review–Geometry Concepts 9.4 Linear Measurement 9.5 Weight and Mass 9.6 Capacity 9.7 Temperature and Conversions Between the U.S. and Metric Systems Exponents and Polynomials 10.1 Adding and Subtracting Polynomials 10.2 Multiplication Properties of Exponents Integrated Review–Operations on Polynomials 10.3 Multiplying Polynomials 10.4 Introduction to Factoring Polynomials Appendix A: Tables A.1 Tables of Geometric Figures A.2 Table of Percents, Decimals, and Fraction Equivalents A.3 Table on Finding Common Percents of a Number A.4 Table of Squares and Square Roots Appendix B: Quotient Rule and Negative Exponents Appendix C: Scientific Notation Appendix D: Geometric Formulas Student Resources Study Skills Builders Bigger Picture–Study Guide Outline Practice Final Exam

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Book SynopsisMarvin Bittinger has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana UniversityPurdue University Indianapolis, and is now professor emeritus of mathematics education. Professor Bittinger has authored over 190 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled Baseball and Mathematics. His hobbies include hiking in Utah, baseball, golf, and bowling. In addition, he also has an interest in philosophy and theology, in particularTable of ContentsTable of Contents Index of Activities Index of Animations Preface Index of Applications JUST-IN-TIME REVIEW The Set of Real Numbers Order for the Real Numbers Graphing Inequalities on the Number Line Absolute Value Add Real Numbers Opposites, or Additive Inverses Subtract Real Numbers Multiply Real Numbers Divide Real Numbers Exponential Notation (Part 1) Order of Operations Translate to an Algebraic Expression Evaluate Algebraic Expressions Equivalent Fraction Expressions The Commutative Laws and the Associative Laws The Distributive Laws Collecting Like Terms Removing Parentheses and Collecting Like Terms Exponential Notation (Part 2) Scientific Notation SOLVING LINEAR EQUATIONS AND INEQUALITIES 1.1 Solving Equations 1.2 Formulas and Applications 1.3 Applications and Problem Solving Mid-Chapter Review 1.4 Sets, Inequalities, and Interval Notation Translating for Success 1.5 Intersections, Unions, and Compound Inequalities 1.6 Absolute-Value Equations and Inequalities Summary and Review Test GRAPHS, FUNCTIONS, AND APPLICATIONS 2.1 Graphs of Equations 2.2 Functions and Graphs 2.3 Finding Domain and Range Mid-Chapter Review 2.4 Linear Functions: Graphs and Slope 2.5 More on Graphing Linear Equations Visualizing for Success 2.6 Finding Equations of Lines; Applications Summary and Review Test Cumulative Review SYSTEMS OF EQUATIONS 3.1 Systems of Equations in Two Variables 3.2 Solving by Substitution 3.3 Solving by Elimination 3.4 Solving Applied Problems: Two Equations Translating for Success Mid-Chapter Review 3.5 Systems of Equations in Three Variables 3.6 Solving Applied Problems: Three Equations 3.7 Systems of Inequalities in Two Variables Visualizing for Success Summary and Review Test Cumulative Review POLYNOMIALS AND POLYNOMIAL FUNCTIONS 4.1 Introduction to Polynomials and Polynomial Functions 4.2 Multiplication of Polynomials 4.3 Introduction to Factoring 4.4 Factoring Trinomials: x2 + bx + c Mid-Chapter Review 4.5 Factoring Trinomials: ax2 + bx + c, a ≠1 4.6 Special Factoring Visualizing for Success 4.7 Factoring: A General Strategy 4.8 Applications of Polynomial Equations and Functions Translating for Success Summary and Review Test Cumulative Review RATIONAL EXPRESSIONS, EQUATIONS, AND FUNCTIONS 5.1 Rational Expressions and Functions: Multiplying, Dividing, and Simplifying 5.2 LCMs, LCDs, Addition, and Subtraction 5.3 Division of Polynomials 5.4 Complex Rational Expressions Mid-Chapter Review 5.5 Solving Rational Equations 5.6 Applications and Proportions Translating for Success 5.7 Formulas and Applications 5.8 Variation and Applications Summary and Review Test Cumulative Review RADICAL EXPRESSIONS, EQUATIONS, AND FUNCTIONS 6.1 Radical Expressions and Functions 6.2 Rational Numbers as Exponents 6.3 Simplifying Radical Expressions 6.4 Addition, Subtraction, and More Multiplication Mid-Chapter Review 6.5 More on Division of Radical Expressions 6.6 Solving Radical Equations 6.7 Applications Involving Powers and Roots Translating for Success 6.8 The Complex Numbers Summary and Review Test Cumulative Review QUADRATIC EQUATIONS AND FUNCTIONS 7.1 The Basics of Solving Quadratic Equations 7.2 The Quadratic Formula 7.3 Applications Involving Quadratic Equations Translating for Success 7.4 More on Quadratic Equations Mid-Chapter Review 7.5 Graphing f(x) = a(x - h)2 + k 7.6 Graphingf(x) = a x2 + bx + c Visualizing for Success 7.7 Mathematical Modeling with Quadratic Functions 7.8 Polynomial Inequalities and Rational Inequalities Summary and Review Test Cumulative Review EXPONENTIAL FUNCTIONS AND LOGARITHMIC FUNCTIONS 8.1 Exponential Functions 8.2 Composite Functions and Inverse Functions 8.3 Logarithmic Functions 8.4 Properties of Logarithmic Functions Mid-Chapter Review 8.5 Natural Logarithmic Functions Visualizing for Success 8.6 Solving Exponential Equations and Logarithmic Equations 8.7 Mathematical Modeling with Exponential Functions and Logarithmic Functions Translating for Success Summary and Review Test Cumulative Review CONIC SECTIONS 9.1 Parabolas and Circles 9.2 Ellipses Mid-Chapter Review 9.3 Hyperbolas Visualizing for Success 9.4 Nonlinear Systems of Equations Summary and Review Test Cumulative Review APPENDIXES Fraction Notation Determinants and Cramer’s Rule Elimination Using Matrices The Algebra of Functions Answers Guided Solutions Glossary Index

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Book SynopsisTable of ContentsTable of Contents Linear Equations and Linear Functions 1.1 Using Qualitative Graphs to Describe Situations 1.2 Graphing Linear Equations 1.3 Slope of a Line 1.4 Meaning of Slope for Equations, Graphs, and Tables 1.5 Finding Linear Equations 1.6 Functions Modeling With Linear Functions 2.1 Using Lines to Model Data 2.2 Finding Equations of Linear Models 2.3 Function Notation and Making Predictions 2.4 Slope Is a Rate of Change Taking It to the Lab: Climate Change Lab • Used-Car Lab • Golf Ball Lab • Walking Student Lab • Linear Lab: Topic of Your Choice Systems of Linear Equations and Systems of Linear Inequalities 3.1 Using Graphs and Tables to Solve Systems 3.2 Using Substitution and Elimination to Solve Systems 3.3 Using Systems to Model Data 3.4 Value, Interest, and Mixture Problems 3.5 Using Linear Inequalities in One Variable to Make Predictions 3.6 Linear Inequalities in Two Variables; Systems of Linear Inequalities Taking It to the Lab: Climate Change Lab (continued from Chapter 2) • Sports Lab • Truck Lab Exponential Functions 4.1 Properties of Exponents 4.2 Rational Exponents 4.3 Graphing Exponential Functions 4.4 Finding Equations of Exponential Functions 4.5 Using Exponential Functions to Model Data Taking It to the Lab: Stringed Instrument Lab • Cooling Water Lab • Exponential Lab: Topic of Your Choice Logarithmic Functions 5.1 Composite Functions 5.2 Inverse Functions 5.3 Logarithmic Functions 5.4 Properties of Logarithms 5.5 Using the Power Property with Exponential Models to Make Predictions 5.6 More Properties of Logarithms 5.7 Natural Logarithm Taking It to the Lab: China and India Populations Lab • Folding Paper Lab • Exponential/Logarithmic Lab: Topic of Your Choice Polynomial Functions 6.1 Adding and Subtracting Polynomial Expressions and Functions 6.2 Multiplying Polynomial Expressions and Functions 6.3 Dividing Polynomials: Long Division and Synthetic Division 6.4 Factoring Trinomials of the Form x2 + bx + c; Factoring Out the GCF 6.5 Factoring Polynomials 6.6 Factoring Special Binomials; A Factoring Strategy 6.7 Using Factoring to Solve Polynomial Equations Taking It to the Lab: Climate Change Lab (continued from Chapter 3) • Projectile Lab Quadratic Functions 7.1 Graphing Quadratic Functions in Vertex Form 7.2 Graphing Quadratic Functions in Standard Form 7.3 Using the Square Root Property to Solve Quadratic Equations 7.4 Solving Quadratic Equations by Completing the Square 7.5 Using the Quadratic Formula to Solve Quadratic Equations 7.6 Solving Systems of Linear Equations in Three Variables; Finding Quadratic Functions 7.7 Finding Quadratic Models 7.8 Modeling with Quadratic Functions Taking It to the Lab: Climate Change Lab (continued from Chapter 6) • Projectile Lab (continued from Chapter 6) • Projectile Lab (Using a CBR or CBL) • Water Flow Lab • Quadratic Lab: Topic of Your Choice Rational Functions 8.1 Finding the Domains of Rational Functions and Simplifying Rational Expressions 8.2 Multiplying and Dividing Rational Expressions; Converting Units 8.3 Adding and Subtracting Rational Expressions 8.4 Simplifying Complex Rational Expressions 8.5 Solving Rational Equations 8.6 Modeling with Rational Functions 8.7 Variation Taking It to the Lab: Climate Change Lab (continued from Chapter 7) • Illumination Lab • Boyle’s Law Lab Radical Functions 9.1 Simplifying Radical Expressions 9.2 Adding, Subtracting, and Multiplying Radical Expressions 9.3 Rationalizing Denominators and Simplifying Quotients of Radical Expressions 9.4 Graphing and Combining Square Root Functions 9.5 Solving Radical Equations 9.6 Modeling with Square Root Functions Taking It to the Lab: Pendulum Lab Sequences and Series 10.1 Arithmetic Sequences 10.2 Geometric Sequences 10.3 Arithmetic Series 10.4 Geometric Series Taking It to the Lab: Bouncing Ball Lab • Stacked Cups Lab Additional Topics 11.1 Absolute Value: Equations and Inequalities 11.2 Performing Operations with Complex Numbers 11.3 Pythagorean Theorem, Distance Formula, and Circles 11.4 Ellipses and Hyperbolas 11.5 Solving Nonlinear Systems of Equations Appendix A: Reviewing the Prerequisite Material Appendix B: Using a TI-83 or TI- 84 Graphing Calculator Appendix C: Using StatCrunch

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Book Synopsis

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Book SynopsisTable of ContentsTable of Contents Basic Concepts 1.1 Study Skills for Success in Mathematics, and Using a Calculator 1.2 Sets and Other Basic Concepts 1.3 Properties of and Operations with Real Numbers 1.4 Order of Operations Mid-Chapter Test: Sections 1.1—1.4 1.5 Exponents 1.6 Scientific Notation Equations and Inequalities 2.1 Solving Linear Equations 2.2 Problem Solving and Using Formulas 2.3 Applications of Algebra Mid-Chapter Test: Sections 2.1—2.3 2.4 Additional Application Problems 2.5 Solving Linear Inequalities 2.6 Solving Equations and Inequalities Containing Absolute Values Graphs and Functions 3.1 Graphs 3.2 Functions 3.3 Linear Functions: Graphs and Applications 3.4 The Slope-Intercept Form of a Linear Equation Mid-Chapter Test: Sections 3.1—3.4 3.5 The Point-Slope Form of a Linear Equation 3.6 The Algebra of Functions 3.7 Graphing Linear Inequalities Systems of Equations and Inequalities 4.1 Solving Systems of Linear Equations in Two Variables 4.2 Solving Systems of Linear Equations in Three Variables 4.3 Systems of Linear Equations: Applications and Problem Solving Mid-Chapter Test: Sections 4.1—4.3 4.4 Solving Systems of Equations Using Matrices 4.5 Solving Systems of Equations Using Determinants and Cramer’s Rule 4.6 Solving Systems of Linear Inequalities Polynomials and Polynomial Functions 5.1 Addition and Subtraction of Polynomials 5.2 Multiplication of Polynomials 5.3 Division of Polynomials and Synthetic Division 5.4 Factoring a Monomial from a Polynomial and Factoring by Grouping Mid-Chapter Test: Sections 5.1—5.4 5.5 Factoring Trinomials 5.6 Special Factoring Formulas 5.7 A General Review of Factoring 5.8 Polynomial Equations Rational Expressions and Equations 6.1 The Domains of Rational Functions and Multiplication and Division of Rational Expressions 6.2 Addition and Subtraction of Rational Expressions 6.3 Complex Fractions 6.4 Solving Rational Equations Mid-Chapter Test: Sections 6.1—6.4 6.5 Rational Equations: Applications and Problem Solving 6.6 Variation Roots, Radicals, and Complex Numbers 7.1 Roots and Radicals 7.2 Rational Exponents 7.3 Simplifying Radicals 7.4 Adding, Subtracting, and Multiplying Radicals Mid-Chapter Test: Sections 7.1—7.4 7.5 Dividing Radicals 7.6 Solving Radical Equations 7.7 Complex Numbers Quadratic Functions 8.1 Solving Quadratic Equations by Completing the Square 8.2 Solving Quadratic Equations by the Quadratic Formula 8.3 Quadratic Equations: Applications and Problem Solving Mid-Chapter Test: Sections 8.1—8.3 8.4 Writing Equations in Quadratic Form 8.5 Graphing Quadratic Functions 8.6 Quadratic and Other Inequalities in One Variable Exponential and Logarithmic Functions 9.1 Composite and Inverse Functions 9.2 Exponential Functions 9.3 Logarithmic Functions 9.4 Properties of Logarithms Mid-Chapter Test: Sections 9.1—9.4 9.5 Common Logarithms 9.6 Exponential and Logarithmic Equations 9.7 Natural Exponential and Natural Logarithmic Functions Conic Sections 10.1 The Parabola and the Circle 10.2 The Ellipse Mid-Chapter Test: Sections 10.1—10.2 10.3 The Hyperbola 10.4 Nonlinear Systems of Equations and Their Applications Sequences, Series, and the Binomial Theorem 11.1 Sequences and Series 11.2 Arithmetic Sequences and Series 11.3 Geometric Sequences and Series Mid-Chapter Test: Sections 11.1—11.3 11.4 The Binomial Theorem Appendix: Geometric Formulas

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Book SynopsisTable of ContentsPreface To the Student 1. Real Numbers 1.1 Study Skills for Success in Mathematics 1.2 Problem Solving 1.3 Fractions 1.4 The Real Number System 1.5 Inequalities Mid-Chapter Test: Sections 1.1-1.5 1.6 Addition of Real Numbers 1.7 Subtraction of Real Numbers 1.8 Multiplication and Division of Real Numbers 1.9 Exponents, Parentheses, and the Order of Operations 1.10 Properties of the Real Number System Chapter 1 Summary Chapter 1 Review Exercises Chapter 1 Practice Test 2. Solving Linear Equations and Inequalities 2.1 Combining Like Terms 2.2 The Addition Property of Equality 2.3 The Multiplication Property of Equality 2.4 Solving Linear Equations with a Variable on Only One Side of the Equation Mid-Chapter Test: Sections 2.1-2.4 2.5 Solving Linear Equations with the Variable on Both Sides of the Equation 2.6 Formulas 2.7 Ratios and Proportions 2.8 Inequalities in One Variable Chapter 2 Summary Chapter 2 Review Exercises Chapter 2 Practice Test Cumulative Review Test 3. Applications of Algebra 3.1 Changing Application Problems into Equations 3.2 Solving Application Problems Mid-Chapter Test: Sections 3.1-3.2 3.3 Geometric Problems 3.4 Motion, Money, and Mixture Problems Chapter 3 Summary Chapter 3 Review Exercises Chapter 3 Practice Test Cumulative Review Test 4. Graphing Linear Equations 4.1 The Cartesian Coordinate System and Linear Equations in Two Variables 4.2 Graphing Linear Equations 4.3 Slope of a Line Mid-Chapter Test: Sections 4.1-4.3 4.4 Slope-Intercept and Point-Slope Forms of a Linear Equation Chapter 4 Summary Chapter 4 Review Exercises Chapter 4 Practice Test Cumulative Review Test 5. Exponents and Polynomials 5.1 Exponents 5.2 Negative Exponents 5.3 Scientific Notation Mid-Chapter Test: Sections 5.1-5.3 5.4 Addition and Subtraction of Polynomials 5.5 Multiplication of Polynomials 5.6 Division of Polynomials Chapter 5 Summary Chapter 5 Review Exercises Chapter 5 Practice Test Cumulative Review Test 6. Factoring 6.1 Factoring a Monomial from a Polynomial 6.2 Factoring by Grouping 6.3 Factoring Trinomials of the Form ax2 + bx + c, a = 1 6.4 Factoring Trinomials of the Form ax2 + bx + c, a ≠ 1 Mid-Chapter Test: Sections 6.1-6.4 6.5 Special Factoring Formulas and a General Review of Factoring 6.6 Solving Quadratic Equations Using Factoring 6.7 Applications of Quadratic Equations Chapter 6 Summary Chapter 6 Review Exercises Chapter 6 Practice Test Cumulative Review Test 7. Rational Expressions and Equations 7.1 Simplifying Rational Expressions 7.2 Multiplication and Division of Rational Expressions 7.3 Addition and Subtraction of Rational Expressions with a Common Denominator and Finding the Least Common Denominator 7.4 Addition and Subtraction of Rational Expressions Mid-Chapter Test: Sections 7.1-7.4 7.5 Complex Fractions 7.6 Solving Rational Equations 7.7 Rational Equations: Applications and Problem Solving 7.8 Variation Chapter 7 Summary Chapter 7 Review Exercises Chapter 7 Practice Test Cumulative Review Test 8. Functions and Their Graphs 8.1 More on Graphs 8.2 Functions 8.3 Linear Functions Mid-Chapter Test: Sections 8.1-8.3 8.4 Slope, Modeling, and Linear Relationships 8.5 The Algebra of Functions Chapter 8 Summary Chapter 8 Review Exercises Chapter 8 Practice Test Cumulative Review Test 9. Systems of Linear Equations 9.1 Solving Systems of Equations Graphically 9.2 Solving Systems of Equations by Substitution 9.3 Solving Systems of Equations by the Addition Method 9.4 Solving Systems of Linear Equations in Three Variables Mid-Chapter Test: Sections 9.1-9.4 9.5 Systems of Linear Equations: Applications and Problem Solving 9.6 Solving Systems of Equations Using Matrices 9.7 Solving Systems of Equations Using Determinants and Cramer’s Rule Chapter 9 Summary Chapter 9 Review Exercises Chapter 9 Practice Test Cumulative Review Test 10. Inequalities in One and Two Variables 10.1 Solving Linear Inequalities in One Variable 10.2 Solving Equations and Inequalities Containing Absolute Values Mid-Chapter Test: Sections 10.1-10.2 10.3 Graphing Linear Inequalities in Two Variables and Systems of Linear Inequalities Chapter 10 Summary Chapter 10 Review Exercises Chapter 10 Practice Test Cumulative Review Test 11. Roots, Radicals, and Complex Numbers 11.1 Roots and Radicals 11.2 Rational Exponents 11.3 Simplifying Radicals 11.4 Adding, Subtracting, and Multiplying Radicals Mid-Chapter Test: Sections 11.1-11.4 11.5 Dividing Radicals 11.6 Solving Radical Equations 11.7 Complex Numbers Chapter 11 Summary Chapter 11 Review Exercises Chapter 11 Practice Test Cumulative Review Test 12. Quadratic Functions 12.1 Solving Quadratic Equations by Completing the Square 12.2 Solving Quadratic Equations by the Quadratic Formula 12.3 Quadratic Equations: Applications and Problem Solving Mid-Chapter Test: Sections 12.1-12.3 12.4 Factoring Expressions and Solving Equations That Are Quadratic in Form 12.5 Graphing Quadratic Functions 12.6 Quadratic, Polynomial, and Rational Inequalities in One Variable Chapter 12 Summary Chapter 12 Review Exercises Chapter 12 Practice Test Cumulative Review Test 13. Exponential and Logarithmic Functions 13.1 Composite and Inverse Functions 13.2 Exponential Functions 13.3 Logarithmic Functions 13.4 Properties of Logarithms Mid-Chapter Test: Sections 13.1-13.4 13.5 Common Logarithms 13.6 Exponential and Logarithmic Equations 13.7 Natural Exponential and Natural Logarithmic Functions Chapter 13 Summary Chapter 13 Review Exercises Chapter 13 Practice Test Cumulative Review Test 14. Conic Sections 14.1 The Parabola and the Circle 14.2 The Ellipse Mid-Chapter Test: Sections 14.1-14.2 14.3 The Hyperbola 14.4 Nonlinear Systems of Equations and Their Applications Chapter 14 Summary Chapter 14 Review Exercises Chapter 14 Practice Test Cumulative Review Test 15. Sequences, Series, and the Binomial Theorem 15.1 Sequences and Series 15.2 Arithmetic Sequences and Series 15.3 Geometric Sequences and Series Mid-Chapter Test: Sections 15.1-15.3 15.4 The Binomial Theorem Chapter 15 Summary Chapter 15 Review Exercises Chapter 15 Practice Test Cumulative Review Test APPENDICES Review of Decimals and Percent Finding the Greatest Common Factor and Least Common Denominator Geometry Review of Exponents, Polynomials, and Factoring Answers Applications Index Subject Index

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Book SynopsisIncludes Extension Exercises, Exploration Activities, Conceptual Exercises, and Group Activities. This workbook isavailable in MyLab Math, or can be packaged in printed form with a text or MyLab Math code.Table of ContentsTable of Contents The Whole Numbers 1.1 Study Skill Tips for Success in Mathematics 1.2 Place Value, Names for Numbers, and Reading Tables 1.3 Adding Whole Numbers and Perimeter 1.4 Subtracting Whole Numbers 1.5 Rounding and Estimating 1.6 Multiplying Whole Numbers and Area 1.7 Dividing Whole Numbers Integrated Review—Operations on Whole Numbers 1.8 An Introduction to Problem Solving 1.9 Exponents, Square Roots, and Order of Operations Multiplying and Dividing Fractions 2.1 Introduction to Fractions and Mixed Numbers 2.2 Factors and Prime Factorization 2.3 Simplest Form of a Fraction Integrated Review—Summary on Fractions, Mixed Numbers, and Factors 2.4 Multiplying Fractions and Mixed Numbers 2.5 Dividing Fractions and Mixed Numbers Adding and Subtracting Fractions 3.1 Adding and Subtracting Like Fractions 3.2 Least Common Multiple 3.3 Adding and Subtracting Unlike Fractions Integrated Review—Operations on Fractions and Mixed Numbers 3.4 Adding and Subtracting Mixed Numbers 3.5 Order, Exponents, and the Order of Operations 3.6 Fractions and Problem Solving Decimals 4.1 Introduction to Decimals 4.2 Order and Rounding 4.3 Adding and Subtracting Decimals 4.4 Multiplying Decimals and Circumference of a Circle Integrated Review—Operations on Decimals 4.5 Dividing Decimals and Order of Operations 4.6 Fractions and Decimals Ratio and Proportion 5.1 Ratios 5.2 Rates Integrated Review— Ratio and Rate 5.3 Proportions 5.4 Proportions and Problem Solving Percent 6.1 Introduction to Percent 6.2 Percents and Fractions 6.3 Solving Percent Problems Using Equations 6.4 Solving Percent Problems Using Proportions Integrated Review—Percent and Percent Problems 6.5 Applications of Percent 6.6 Percent and Problem Solving: Sales Tax, Commission, and Discount 6.7 Percent and Problem Solving: Interest Measurement 7.1 Length: U.S. and Metric Systems of Measurement 7.2 Weight and Mass: U.S. and Metric Systems of Measurement 7.3 Capacity: U.S. and Metric Systems of Measurement Integrated Review—Length, Weight, and Capacity 7.4 Conversions Between the U.S. and Metric Systems 7.5 Temperature: U.S. and Metric Systems of Measurement 7.6 Energy: U.S. and Metric Systems of Measurement Geometry 8.1 Lines and Angles 8.2 Plane Figures and Solids 8.3 Perimeter 8.4 Area 8.5 Volume Integrated Review—Geometry Concepts 8.6 Square Roots and the Pythagorean Theorem 8.7 Congruent and Similar Triangles Reading Graphs and Introduction to Statistics and Probability 9.1 Pictographs, Bar Graphs, Histograms, and Line Graphs 9.2 Circle Graphs Integrated Review—Reading Graphs 9.3 Mean, Median, Mode, and Range 9.4 Counting and Introduction to Probability Signed Numbers 10.1 Signed Numbers 10.2 Adding Signed Numbers 10.3 Subtracting Signed Numbers Integrated Review—Signed Numbers 10.4 Multiplying and Dividing Signed Numbers 10.5 Order of Operations Introduction to Algebra 11.1 Introduction to Variables 11.2 Solving Equations: The Addition Property 11.3 Solving Equations: The Multiplication Property Integrated Review—Expressions and Equations 11.4 Solving Equations Using Addition and Multiplication Properties 11.5 Equations and Problem Solving Appendix A: Tables A.1 Addition Table and One Hundred Addition Facts A.2 Multiplication Table and One Hundred Multiplication Facts A.3 Table of Geometric Figures A.4 Table of Percents, Decimals, and Fraction Equivalents A.5 Table on Finding Common Percents of a Number A.6 Table of Squares and Square Roots A.7 Compound Interest Table Appendix B: Unit Analysis Student Resources Study Skills Builders Bigger Picture—Study Guide Outline Practice Final Exam

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Book Synopsis For courses in Beginning and Intermediate Algebra (Combined Courses). Balancing skills and concepts The Lial Developmental Algebra Series uses a teacherly writing style and a careful blend of skills development and conceptual questions to meet the unique needs of the developmental math student. The author team takes advantage of experiences in the classroom and an editing eye to offer one of the most well-rounded series available, written with the developmental learner in mind. In this revision, the team retains their hallmark writing style, and provides new features and resources to optimize student preparedness and conceptual understanding. The Lial program provides students with the perfeTable of ContentsTable of Contents Study Skill 1: Using Your Math Text Study Skill 2: Reading Your Math Text Study Skill 3: Taking Lecture Notes Study Skill 4: Completing Your Homework Study Skill 5: Using Study Cards Study Skill 6: Managing Your Time Study Skill 7: Reviewing a Chapter Study Skill 8: Taking Math Tests Study Skill 9: Analyzing Your Test Results Study Skill 10: Preparing for Your Math Final Prealgebra Review R.1 Fractions R.2 Decimals and Percents The Real Number System 1.1 Exponents, Order of Operations, and Inequality 1.2 Variables, Expressions, and Equations 1.3 Real Numbers and the Number Line 1.4 Adding and Subtracting Real Numbers 1.5 Multiplying and Dividing Real Numbers Summary Exercises: Performing Operations with Real Numbers 1.6 Properties of Real Numbers 1.7 Simplifying Expressions Chapter 1 Summary Chapter 1 Review Exercises Chapter 1 Mixed Review Exercises Chapter 1 Test Chapters R and 1 Cumulative Review Exercises Linear Equations and Inequalities in One Variable 2.1 The Addition Property of Equality 2.2 The Multiplication Property of Equality 2.3 Solving Linear Equations Using Both Properties of Equality 2.4 Clearing Fractions and Decimals When Solving Linear Equations Summary Exercises: Applying Methods for Solving Linear Equations 2.5 Applications of Linear Equations 2.6 Formulas and Additional Applications from Geometry 2.7 Ratio, Proportion, and Percent 2.8 Further Applications of Linear Equations 2.9 Solving Linear Inequalities Chapter 2 Summary Chapter 2 Review Exercises Chapter 2 Mixed Review Exercises Chapter 2 Test Chapters R–2 Cumulative Review Exercises Linear Equations in Two Variables 3.1 Linear Equations and Rectangular Coordinates 3.2 Graphing Linear Equations in Two Variables 3.3 The Slope of a Line 3.4 Slope-Intercept Form of a Linear Equation 3.5 Point-Slope Form of a Linear Equation and Modeling Summary Exercises: Applying Graphing and Equation-Writing Techniques for Lines Chapter 3 Summary Chapter 3 Review Exercises Chapter 3 Mixed Review Exercises Chapter 3 Test Chapters R–3 Cumulative Review Exercises Exponents and Polynomials 4.1 The Product Rule and Power Rules for Exponents 4.2 Integer Exponents and the Quotient Rule Summary Exercises: Applying the Rules for Exponents 4.3 Scientific Notation 4.4 Adding, Subtracting, and Graphing Polynomials 4.5 Multiplying Polynomials 4.6 Special Products 4.7 Dividing Polynomials Chapter 4 Summary Chapter 4 Review Exercises Chapter 4 Mixed Review Exercises Chapter 4 Test Chapters R–4 Cumulative Review Exercises Factoring and Applications 5.1 Greatest Common Factor; Factoring by Grouping 5.2 Factoring Trinomials 5.3 More on Factoring Trinomials 5.4 Special Factoring Techniques Summary Exercises: Recognizing and Applying Factoring Strategies 5.5 Solving Quadratic Equations Using the Zero-Factor Property 5.6 Applications of Quadratic Equations Chapter 5 Summary Chapter 5 Review Exercises Chapter 5 Mixed Review Exercises Chapter 5 Test Chapters R–5 Cumulative Review Exercises Rational Expressions and Applications 6.1 The Fundamental Property of Rational Expressions 6.2 Multiplying and Dividing Rational Expressions 6.3 Least Common Denominators 6.4 Adding and Subtracting Rational Expressions 6.5 Complex Fractions 6.6 Solving Equations with Rational Expressions Summary Exercises: Simplifying Rational Expressions vs. Solving Rational Equations 6.7 Applications of Rational Expressions Chapter 6 Summary Chapter 6 Review Exercises Chapter 6 Mixed Review Exercises Chapter 6 Test Chapters R–6 Cumulative Review Exercises Linear Equations, Graphs, and Systems 7.1 Review of Graphs and Slopes of Lines 7.2 Review of Equations of Lines; Linear Models 7.3 Solving Systems of Linear Equations by Graphing 7.4 Solving Systems of Linear Equations by Substitution 7.5 Solving Systems of Linear Equations by Elimination Summary Exercises: Applying Techniques for Solving Systems of Linear Equations 7.6 Systems of Linear Equations in Three Variables 7.7 Applications of Systems of Linear Equations Chapter 7 Summary Chapter 7 Review Exercises Chapter 7 Mixed Review Exercises Chapter 7 Test Chapters R–7 Cumulative Review Exercises Inequalities and Absolute Value 8.1 Review of Linear Inequalities in One Variable 8.2 Set Operations and Compound Inequalities 8.3 Absolute Value Equations and Inequalities Summary Exercises: Solving Linear and Absolute Value Equations and Inequalities 8.4 Linear Inequalities and Systems in Two Variables Chapter 8 Summary Chapter 8 Review Exercises Chapter 8 Mixed Review Exercises Chapter 8 Test Chapters R–8 Cumulative Review Exercises Relations and Functions 9.1 Introduction to Relations and Functions 9.2 Function Notation and Linear Functions 9.3 Polynomial Functions, Operations, and Composition 9.4 Variation Chapter 9 Summary Chapter 9 Review Exercises Chapter 9 Mixed Review Exercises Chapter 9 Test Chapters R–9 Cumulative Review Exercises Roots, Radicals, and Root Functions 10.1 Radical Expressions and Graphs 10.2 Rational Exponents 10.3 Simplifying Radicals, the Distance Formula, and Circles 10.4 Adding and Subtracting Radical Expressions 10.5 Multiplying and Dividing Radical Expressions Summary Exercises: Performing Operations with Radicals and Rational Exponents 10.6 Solving Equations with Radicals 10.7 Complex Numbers Chapter 10 Summary Chapter 10 Review Exercises Chapter 10 Mixed Review Exercises Chapter 10 Test Chapters R–10 Cumulative Review Exercises Quadratic Equations, Inequalities, and Functions 11.1 Solving Quadratic Equations by the Square Root Property 11.2 Solving Quadratic Equations by Completing the Square 11.3 Solving Quadratic Equations by the Quadratic Formula 11.4 Equations That Lead to Quadratic Methods Summary Exercises: Applying Methods for Solving Quadratic Equations 11.5 Formulas and Further Applications 11.6 Graphs of Quadratic Functions 11.7 More about Parabolas and Their Applications 11.8 Polynomial and Rational Inequalities Chapter 11 Summary Chapter 11 Review Exercises Chapter 11 Mixed Review Exercises Chapter 11 Test Chapters R–11 Cumulative Review Exercises Inverse, Exponential, and Logarithmic Functions 12.1 Inverse Functions 12.2 Exponential Functions 12.3 Logarithmic Functions 12.4 Properties of Logarithms 12.5 Common and Natural Logarithms 12.6 Exponential and Logarithmic Equations; Further Applications Chapter 12 Summary Chapter 12 Review Exercises Chapter 12 Mixed Review Exercises Chapter 12 Test Chapters R–12 Cumulative Review Exercises Nonlinear Functions, Conic Sections, and Nonlinear Systems 13.1 Additional Graphs of Functions 13.2 Circles Revisited and Ellipses 13.3 Hyperbolas and Functions Defined by Radicals 13.4 Nonlinear Systems of Equations 13.5 Second-Degree Inequalities and Systems of Inequalities Chapter 13 Summary Chapter 13 Review Exercises Chapter 13 Mixed Review Exercises Chapter 13 Test Chapters R—13 Cumulative Review Exercises Further Topics in Algebra 14.1 Sequences and Series 14.2 Arithmetic Sequences 14.3 Geometric Sequences 14.4 The Binomial Theorem Chapter 14 Summary Chapter 14 Review Exercises Chapter 14 Mixed Review Exercises Chapter 14 Test Chapters R—14 Cumulative Review Exercises

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Book SynopsisStudent Solutions Manual Provides completely worked-out solutions to the odd-numbered section exercises and to all exercises in the Now Trys, Relating Concepts, Chapter Reviews, Mixed Review, Chapter Tests, and Cumulative Reviews. Table of ContentsTable of Contents Study Skill 1: Using Your Math Text Study Skill 2: Reading Your Math Text Study Skill 3: Taking Lecture Notes Study Skill 4: Completing Your Homework Study Skill 5: Using Study Cards Study Skill 6: Managing Your Time Study Skill 7: Reviewing a Chapter Study Skill 8: Taking Math Tests Study Skill 9: Analyzing Your Test Results Study Skill 10: Preparing for Your Math Final Review of the Real Number System R.1 Fractions, Decimals, and Percents R.2 Basic Concepts from Algebra R.3 Operations on Real Numbers R.3 Exponents, Roots, and Order of Operations R.4 Properties of Real Numbers Chapter R Summary Chapter R Test Linear Equations, Inequalities, and Applications 1.1 Linear Equations in One Variable 1.2 Formulas and Percent 1.3 Applications of Linear Equations 1.4 Further Applications of Linear Equations Summary Exercises: Applying Problem-Solving Techniques 1.5 Linear Inequalities in One Variable 1.6 Set Operations and Compound Inequalities 1.7 Absolute Value Equations and Inequalities Summary Exercises: Solving Linear and Absolute Value Equations and Inequalities Chapter 1 Summary Chapter 1 Review Exercises Chapter 1 Mixed Review Exercises Chapter 1 Test Chapters R and 1 Cumulative Review Exercises Linear Equations, Graphs, and Functions 2.1 Linear Equations in Two Variables Study Skills: Managing Your Time 2.2 The Slope of a Line 2.3 Writing Equations of Lines Summary Exercises: Finding Slopes and Equations of Lines 2.4 Linear Inequalities in Two Variables 2.5 Introduction to Relations and Functions 2.6 Function Notation and Linear Functions Chapter 2 Summary Chapter 2 Review Exercises Chapter 2 Mixed Review Exercises Chapter 2 Test Chapters R–2 Cumulative Review Exercises Systems of Linear Equations 3.1 Systems of Linear Equations in Two Variables 3.2 Systems of Linear Equations in Three Variables 3.3 Applications of Systems of Linear Equations Chapter 3 Summary Chapter 3 Review Exercises Chapter 3 Mixed Review Exercises Chapter 3 Test Chapters R–3 Cumulative Review Exercises Exponents, Polynomials, and Polynomial Functions 4.1 Integer Exponents 4.2 Scientific Notation 4.3 Adding and Subtracting Polynomials 4.4 Polynomial Functions, Graphs, and Composition 4.5 Multiplying Polynomials 4.6 Dividing Polynomials Chapter 4 Summary Chapter 4 Review Exercises Chapter 4 Mixed Review Exercises Chapter 4 Test Chapters R–4 Cumulative Review Exercises Factoring 5.1 Greatest Common Factors and Factoring by Grouping 5.2 Factoring Trinomials 5.3 Special Factoring 5.4 A General Approach to Factoring 5.5 Solving Equations by the Zero-Factor Property Chapter 5 Summary Chapter 5 Review Exercises Chapter 5 Mixed Review Exercises Chapter 5 Test Chapters R–5 Cumulative Review Exercises Rational Expressions and Functions 6.1 Rational Expressions and Functions; Multiplying and Dividing 6.2 Adding and Subtracting Rational Expressions 6.3 Complex Fractions 6.4 Equations with Rational Expressions and Graphs Summary Exercises: Simplifying Rational Expressions vs. Solving Rational Equations 6.5 Applications of Rational Expressions 6.6 Variation Chapter 6 Summary Chapter 6 Review Exercises Chapter 6 Mixed Review Exercises Chapter 6 Test Chapters R–6 Cumulative Review Exercises Roots, Radicals, and Root Functions 7.1 Radical Expressions and Graphs 7.2 Rational Exponents 7.3 Simplifying Radicals, the Distance Formula, and Circles 7.4 Adding and Subtracting Radical Expressions 7.5 Multiplying and Dividing Radical Expressions Summary Exercises: Performing Operations with Radicals and Rational Exponents 7.6 Solving Equations with Radicals 7.7 Complex Numbers Chapter 7 Summary Chapter 7 Review Exercises Chapter 7 Mixed Review Exercises Chapter 7 Test Chapters R–7 Cumulative Review Exercises Quadratic Equations, Inequalities, and Functions 8.1 The Square Root Property and Completing the Square 8.2 The Quadratic Formula 8.3 Equations That Lead to Quadratic Methods Summary Exercises: Applying Methods for Solving Quadratic Equations 8.4 Formulas and Further Applications 8.5 Graphs of Quadratic Functions 8.6 More about Parabolas and Their Applications 8.7 Polynomial and Rational Inequalities Chapter 8 Summary Chapter 8 Review Exercises Chapter 8 Mixed Review Exercises Chapter 8 Test Chapters R–8 Cumulative Review Exercises Inverse, Exponential, and Logarithmic Functions 9.1 Inverse Functions 9.2 Exponential Functions 9.3 Logarithmic Functions 9.4 Properties of Logarithms 9.5 Common and Natural Logarithms 9.6 Exponential and Logarithmic Equations; Further Applications Chapter 9 Summary Chapter 9 Review Exercises Chapter 9 Mixed Review Exercises Chapter 9 Test Chapters R–9 Cumulative Review Exercises Nonlinear Functions, Conic Sections, and Nonlinear Systems 10.1 Additional Graphs of Functions 10.2 Circles Revisited and Ellipses 10.3 Hyperbolas and Functions Defined by Radicals 10.4 Nonlinear Systems of Equations 10.5 Second-Degree Inequalities and Systems of Inequalities Chapter 10 Summary Chapter 10 Review Exercises Chapter 10 Mixed Review Exercises Chapter 10 Test Chapters R-10 Cumulative Review Exercises Further Topics in Algebra 11.1 Sequences and Series 11.2 Arithmetic Sequences 11.3 Geometric Sequences 11.4 The Binomial Theorem Chapter 11 Summary Chapter 11 Review Exercises Chapter 11 Mixed Review Exercises Chapter 11 Test Chapters R-11 Cumulative Review Exercises Appendix A: Synthetic Division Answers to Selected Exercises Credits Index

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Book SynopsisTable of ContentsTable of Contents Study Skill 1: Using Your Math Text Study Skill 2: Reading Your Math Text Study Skill 3: Taking Lecture Notes Study Skill 4: Completing Your Homework Study Skill 5: Using Study Cards Study Skill 6: Managing Your Time Study Skill 7: Reviewing a Chapter Study Skill 8: Taking Math Tests Study Skill 9: Analyzing Your Test Results Study Skill 10: Preparing for Your Math Final Prealgebra Review R.1 Fractions R.2 Decimals and Percents The Real Number System 1.1 Exponents, Order of Operations, and Inequality 1.2 Variables, Expressions, and Equations 1.3 Real Numbers and the Number Line 1.4 Adding and Subtracting Real Numbers 1.5 Multiplying and Dividing Real Numbers Summary Exercises: Performing Operations with Real Numbers 1.6 Properties of Real Numbers 1.7 Simplifying Expressions Chapter 1 Summary Chapter 1 Review Exercises Chapter 1 Mixed Review Exercises Chapter 1 Test Chapters R and 1 Cumulative Review Exercises Linear Equations and Inequalities in One Variable 2.1 The Addition Property of Equality 2.2 The Multiplication Property of Equality 2.3 Solving Linear Equations Using Both Properties of Equality 2.4 Clearing Fractions and Decimals When Solving Linear Equations Summary Exercises: Applying Methods for Solving Linear Equations 2.5 Applications of Linear Equations 2.6 Formulas and Additional Applications from Geometry 2.7 Ratio, Proportion, and Percent 2.8 Further Applications of Linear Equations 2.9 Solving Linear Inequalities Chapter 2 Summary Chapter 2 Review Exercises Chapter 2 Mixed Review Exercises Chapter 2 Test Chapters R–2 Cumulative Review Exercises Linear Equations in Two Variables 3.1 Linear Equations and Rectangular Coordinates 3.2 Graphing Linear Equations in Two Variables 3.3 The Slope of a Line 3.4 Slope-Intercept Form of a Linear Equation 3.5 Point-Slope Form of a Linear Equation and Modeling Summary Exercises: Applying Graphing and Equation-Writing Techniques for Lines Chapter 3 Summary Chapter 3 Review Exercises Chapter 3 Mixed Review Exercises Chapter 3 Test Chapters R–3 Cumulative Review Exercises Exponents and Polynomials 4.1 The Product Rule and Power Rules for Exponents 4.2 Integer Exponents and the Quotient Rule Summary Exercises: Applying the Rules for Exponents 4.3 Scientific Notation 4.4 Adding, Subtracting, and Graphing Polynomials 4.5 Multiplying Polynomials 4.6 Special Products 4.7 Dividing Polynomials Chapter 4 Summary Chapter 4 Review Exercises Chapter 4 Mixed Review Exercises Chapter 4 Test Chapters R–4 Cumulative Review Exercises Factoring and Applications 5.1 Greatest Common Factor; Factoring by Grouping 5.2 Factoring Trinomials 5.3 More on Factoring Trinomials 5.4 Special Factoring Techniques Summary Exercises: Recognizing and Applying Factoring Strategies 5.5 Solving Quadratic Equations Using the Zero-Factor Property 5.6 Applications of Quadratic Equations Chapter 5 Summary Chapter 5 Review Exercises Chapter 5 Mixed Review Exercises Chapter 5 Test Chapters R–5 Cumulative Review Exercises Rational Expressions and Applications 6.1 The Fundamental Property of Rational Expressions 6.2 Multiplying and Dividing Rational Expressions 6.3 Least Common Denominators 6.4 Adding and Subtracting Rational Expressions 6.5 Complex Fractions 6.6 Solving Equations with Rational Expressions Summary Exercises: Simplifying Rational Expressions vs. Solving Rational Equations 6.7 Applications of Rational Expressions Chapter 6 Summary Chapter 6 Review Exercises Chapter 6 Mixed Review Exercises Chapter 6 Test Chapters R–6 Cumulative Review Exercises Linear Equations, Graphs, and Systems 7.1 Review of Graphs and Slopes of Lines 7.2 Review of Equations of Lines; Linear Models 7.3 Solving Systems of Linear Equations by Graphing 7.4 Solving Systems of Linear Equations by Substitution 7.5 Solving Systems of Linear Equations by Elimination Summary Exercises: Applying Techniques for Solving Systems of Linear Equations 7.6 Systems of Linear Equations in Three Variables 7.7 Applications of Systems of Linear Equations Chapter 7 Summary Chapter 7 Review Exercises Chapter 7 Mixed Review Exercises Chapter 7 Test Chapters R–7 Cumulative Review Exercises Inequalities and Absolute Value 8.1 Review of Linear Inequalities in One Variable 8.2 Set Operations and Compound Inequalities 8.3 Absolute Value Equations and Inequalities Summary Exercises: Solving Linear and Absolute Value Equations and Inequalities 8.4 Linear Inequalities and Systems in Two Variables Chapter 8 Summary Chapter 8 Review Exercises Chapter 8 Mixed Review Exercises Chapter 8 Test Chapters R–8 Cumulative Review Exercises Relations and Functions 9.1 Introduction to Relations and Functions 9.2 Function Notation and Linear Functions 9.3 Polynomial Functions, Operations, and Composition 9.4 Variation Chapter 9 Summary Chapter 9 Review Exercises Chapter 9 Mixed Review Exercises Chapter 9 Test Chapters R–9 Cumulative Review Exercises Roots, Radicals, and Root Functions 10.1 Radical Expressions and Graphs 10.2 Rational Exponents 10.3 Simplifying Radicals, the Distance Formula, and Circles 10.4 Adding and Subtracting Radical Expressions 10.5 Multiplying and Dividing Radical Expressions Summary Exercises: Performing Operations with Radicals and Rational Exponents 10.6 Solving Equations with Radicals 10.7 Complex Numbers Chapter 10 Summary Chapter 10 Review Exercises Chapter 10 Mixed Review Exercises Chapter 10 Test Chapters R–10 Cumulative Review Exercises Quadratic Equations, Inequalities, and Functions 11.1 Solving Quadratic Equations by the Square Root Property 11.2 Solving Quadratic Equations by Completing the Square 11.3 Solving Quadratic Equations by the Quadratic Formula 11.4 Equations That Lead to Quadratic Methods Summary Exercises: Applying Methods for Solving Quadratic Equations 11.5 Formulas and Further Applications 11.6 Graphs of Quadratic Functions 11.7 More about Parabolas and Their Applications 11.8 Polynomial and Rational Inequalities Chapter 11 Summary Chapter 11 Review Exercises Chapter 11 Mixed Review Exercises Chapter 11 Test Chapters R–11 Cumulative Review Exercises Inverse, Exponential, and Logarithmic Functions 12.1 Inverse Functions 12.2 Exponential Functions 12.3 Logarithmic Functions 12.4 Properties of Logarithms 12.5 Common and Natural Logarithms 12.6 Exponential and Logarithmic Equations; Further Applications Chapter 12 Summary Chapter 12 Review Exercises Chapter 12 Mixed Review Exercises Chapter 12 Test Chapters R–12 Cumulative Review Exercises Nonlinear Functions, Conic Sections, and Nonlinear Systems 13.1 Additional Graphs of Functions 13.2 Circles Revisited and Ellipses 13.3 Hyperbolas and Functions Defined by Radicals 13.4 Nonlinear Systems of Equations 13.5 Second-Degree Inequalities and Systems of Inequalities Chapter 13 Summary Chapter 13 Review Exercises Chapter 13 Mixed Review Exercises Chapter 13 Test Chapters R—13 Cumulative Review Exercises Further Topics in Algebra 14.1 Sequences and Series 14.2 Arithmetic Sequences 14.3 Geometric Sequences 14.4 The Binomial Theorem Chapter 14 Summary Chapter 14 Review Exercises Chapter 14 Mixed Review Exercises Chapter 14 Test Chapters R—14 Cumulative Review Exercises

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Book SynopsisTable of ContentsTable of Contents Study Skill 1: Using Your Math Text Study Skill 2: Reading Your Math Text Study Skill 3: Taking Lecture Notes Study Skill 4: Completing Your Homework Study Skill 5: Using Study Cards Study Skill 6: Managing Your Time Study Skill 7: Reviewing a Chapter Study Skill 8: Taking Math Tests Study Skill 9: Analyzing Your Test Results Study Skill 10: Preparing for Your Math Final Review of the Real Number System R.1 Fractions, Decimals, and Percents R.2 Basic Concepts from Algebra R.3 Operations on Real Numbers R.3 Exponents, Roots, and Order of Operations R.4 Properties of Real Numbers Chapter R Summary Chapter R Test Linear Equations, Inequalities, and Applications 1.1 Linear Equations in One Variable 1.2 Formulas and Percent 1.3 Applications of Linear Equations 1.4 Further Applications of Linear Equations Summary Exercises: Applying Problem-Solving Techniques 1.5 Linear Inequalities in One Variable 1.6 Set Operations and Compound Inequalities 1.7 Absolute Value Equations and Inequalities Summary Exercises: Solving Linear and Absolute Value Equations and Inequalities Study Skills: Reviewing a Chapter Chapter 1 Summary Chapter 1 Review Exercises Chapter 1 Mixed Review Exercises Chapter 1 Test Chapters R and 1 Cumulative Review Exercises Linear Equations, Graphs, and Functions 2.1 Linear Equations in Two Variables 2.2 The Slope of a Line 2.3 Writing Equations of Lines Summary Exercises: Finding Slopes and Equations of Lines 2.4 Linear Inequalities in Two Variables 2.5 Introduction to Relations and Functions 2.6 Function Notation and Linear Functions Chapter 2 Summary Chapter 2 Review Exercises Chapter 2 Mixed Review Exercises Chapter 2 Test Chapters R—2 Cumulative Review Exercises Systems of Linear Equations 3.1 Systems of Linear Equations in Two Variables 3.2 Systems of Linear Equations in Three Variables 3.3 Applications of Systems of Linear Equations Chapter 3 Summary Chapter 3 Review Exercises Chapter 3 Mixed Review Exercises Chapter 3 Test Chapters R–3 Cumulative Review Exercises Exponents, Polynomials, and Polynomial Functions 4.1 Integer Exponents and Scientific Notation 4.2 Adding and Subtracting Polynomials 4.3 Polynomial Functions, Graphs, and Composition 4.4 Multiplying Polynomials 4.5 Dividing Polynomials Chapter 4 Summary Chapter 4 Review Exercises Chapter 4 Mixed Review Exercises Chapter 4 Test Chapters R–4 Cumulative Review Exercises Factoring 5.1 Greatest Common Factors and Factoring by Grouping 5.2 Factoring Trinomials 5.3 Special Factoring 5.4 A General Approach to Factoring 5.5 Solving Equations by the Zero-Factor Property Chapter 5 Summary Chapter 5 Review Exercises Chapter 5 Mixed Review Exercises Chapter 5 Test Chapters R–5 Cumulative Review Exercises Rational Expressions and Functions 6.1 Rational Expressions and Functions; Multiplying and Dividing 6.2 Adding and Subtracting Rational Expressions 6.3 Complex Fractions 6.4 Equations with Rational Expressions and Graphs Summary Exercises: Simplifying Rational Expressions vs. Solving Rational Equations 6.5 Applications of Rational Expressions 6.6 Variation Chapter 6 Summary Chapter 6 Review Exercises Chapter 6 Mixed Review Exercises Chapter 6 Test Chapters R–6 Cumulative Review Exercises Roots, Radicals, and Root Functions 7.1 Radical Expressions and Graphs 7.2 Rational Exponents 7.3 Simplifying Radicals, the Distance Formula, and Circles 7.4 Adding and Subtracting Radical Expressions 7.5 Multiplying and Dividing Radical Expressions Summary Exercises: Performing Operations with Radicals and Rational Exponents 7.6 Solving Equations with Radicals 7.7 Complex Numbers Chapter 7 Summary Chapter 7 Review Exercises Chapter 7 Mixed Review Exercises Chapter 7 Test Chapters R–7 Cumulative Review Exercises Quadratic Equations and Inequalities 8.1 The Square Root Property and Completing the Square 8.2 The Quadratic Formula 8.3 Equations That Lead to Quadratic Methods Summary Exercises: Applying Methods for Solving Quadratic Equations 8.4 Formulas and Further Applications 8.5 Polynomial and Rational Inequalities Chapter 8 Summary Chapter 8 Review Exercises Chapter 8 Mixed Review Exercises Chapter 8 Test Chapters R–8 Cumulative Review Exercises Additional Graphs of Functions and Relations 9.1 Review of Operations and Composition 9.2 Graphs of Quadratic Functions 9.3 More About Parabolas and Their Applications 9.4 Symmetry; Increasing and Decreasing Functions 9.5 Piecewise Linear Functions Chapter 9 Summary Chapter 9 Review Exercises Chapter 9 Mixed Review Exercises Chapter 9 Test Chapters R–9 Cumulative Review Exercises Inverse, Exponential, and Logarithmic Functions 10.1 Inverse Functions 10.2 Exponential Functions 10.3 Logarithmic Functions 10.4 Properties of Logarithms 10.5 Common and Natural Logarithms 10.6 Exponential and Logarithmic Equations; Further Applications Chapter 10 Summary Chapter 10 Review Exercises Chapter 10 Mixed Review Exercises Chapter 10 Test Chapters R–10 Cumulative Review Exercises Polynomial and Rational Functions 11.1 Zeros of Polynomial Functions (I) 11.2 Zeros of Polynomial Functions (II) 11.3 Graphs and Applications of Polynomial Functions Summary Exercises: Examining Polynomial Functions and Graphs 11.4 Graphs and Applications of Rational Functions Chapter 11 Summary Chapter 11 Review Exercises Chapter 11 Mixed Review Exercises Chapter 11 Test Chapters R–11 Cumulative Review Exercises Conic Sections and Nonlinear Systems 12.1 Circles Revisited and Ellipses 12.2 Hyperbolas and Functions Defined by Radicals 12.3 Nonlinear Systems of Equations 12.4 Second-Degree Inequalities, Systems of Inequalities, and Linear Programming Chapter 12 Summary Chapter 12 Review Exercises Chapter 12 Mixed Review Exercises Chapter 12 Test Chapters R–12 Cumulative Review Exercises Further Topics in Algebra 13.1 Sequences and Series 13.2 Arithmetic Sequences 13.3 Geometric Sequences 13.4 The Binomial Theorem 13.5 Mathematical Induction 13.6 Counting Theory 13.7 Basics of Probability Chapter 13 Summary Chapter 13 Review Exercises Chapter 13 Mixed Review Exercises Chapter 13 Test Chapters R–13 Cumulative Review Exercises Appendix A: Solving Systems of Linear Equations by Matrix Methods Appendix B: Determinants and Cramer’s Rule Appendix C: Properties of Matrices Appendix D: Matrix Inverses Photo Credits Answers to Selected Exercises Index

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Book SynopsisTable of ContentsTable of Contents Study Skill 1: Using Your Math Text Study Skill 2: Reading Your Math Text Study Skill 3: Taking Lecture Notes Study Skill 4: Completing Your Homework Study Skill 5: Using Study Cards Study Skill 6: Managing Your Time Study Skill 7: Reviewing a Chapter Study Skill 8: Taking Math Tests Study Skill 9: Analyzing Your Test Results Study Skill 10: Preparing for Your Math Final Review of the Real Number System R.1 Fractions, Decimals, and Percents R.2 Basic Concepts from Algebra R.3 Operations on Real Numbers R.3 Exponents, Roots, and Order of Operations R.4 Properties of Real Numbers Chapter R Summary Chapter R Test Linear Equations, Inequalities, and Applications 1.1 Linear Equations in One Variable 1.2 Formulas and Percent 1.3 Applications of Linear Equations 1.4 Further Applications of Linear Equations Summary Exercises: Applying Problem-Solving Techniques 1.5 Linear Inequalities in One Variable 1.6 Set Operations and Compound Inequalities 1.7 Absolute Value Equations and Inequalities Summary Exercises: Solving Linear and Absolute Value Equations and Inequalities Study Skills: Reviewing a Chapter Chapter 1 Summary Chapter 1 Review Exercises Chapter 1 Mixed Review Exercises Chapter 1 Test Chapters R and 1 Cumulative Review Exercises Linear Equations, Graphs, and Functions 2.1 Linear Equations in Two Variables 2.2 The Slope of a Line 2.3 Writing Equations of Lines Summary Exercises: Finding Slopes and Equations of Lines 2.4 Linear Inequalities in Two Variables 2.5 Introduction to Relations and Functions 2.6 Function Notation and Linear Functions Chapter 2 Summary Chapter 2 Review Exercises Chapter 2 Mixed Review Exercises Chapter 2 Test Chapters R—2 Cumulative Review Exercises Systems of Linear Equations 3.1 Systems of Linear Equations in Two Variables 3.2 Systems of Linear Equations in Three Variables 3.3 Applications of Systems of Linear Equations Chapter 3 Summary Chapter 3 Review Exercises Chapter 3 Mixed Review Exercises Chapter 3 Test Chapters R–3 Cumulative Review Exercises Exponents, Polynomials, and Polynomial Functions 4.1 Integer Exponents and Scientific Notation 4.2 Adding and Subtracting Polynomials 4.3 Polynomial Functions, Graphs, and Composition 4.4 Multiplying Polynomials 4.5 Dividing Polynomials Chapter 4 Summary Chapter 4 Review Exercises Chapter 4 Mixed Review Exercises Chapter 4 Test Chapters R–4 Cumulative Review Exercises Factoring 5.1 Greatest Common Factors and Factoring by Grouping 5.2 Factoring Trinomials 5.3 Special Factoring 5.4 A General Approach to Factoring 5.5 Solving Equations by the Zero-Factor Property Chapter 5 Summary Chapter 5 Review Exercises Chapter 5 Mixed Review Exercises Chapter 5 Test Chapters R–5 Cumulative Review Exercises Rational Expressions and Functions 6.1 Rational Expressions and Functions; Multiplying and Dividing 6.2 Adding and Subtracting Rational Expressions 6.3 Complex Fractions 6.4 Equations with Rational Expressions and Graphs Summary Exercises: Simplifying Rational Expressions vs. Solving Rational Equations 6.5 Applications of Rational Expressions 6.6 Variation Chapter 6 Summary Chapter 6 Review Exercises Chapter 6 Mixed Review Exercises Chapter 6 Test Chapters R–6 Cumulative Review Exercises Roots, Radicals, and Root Functions 7.1 Radical Expressions and Graphs 7.2 Rational Exponents 7.3 Simplifying Radicals, the Distance Formula, and Circles 7.4 Adding and Subtracting Radical Expressions 7.5 Multiplying and Dividing Radical Expressions Summary Exercises: Performing Operations with Radicals and Rational Exponents 7.6 Solving Equations with Radicals 7.7 Complex Numbers Chapter 7 Summary Chapter 7 Review Exercises Chapter 7 Mixed Review Exercises Chapter 7 Test Chapters R–7 Cumulative Review Exercises Quadratic Equations and Inequalities 8.1 The Square Root Property and Completing the Square 8.2 The Quadratic Formula 8.3 Equations That Lead to Quadratic Methods Summary Exercises: Applying Methods for Solving Quadratic Equations 8.4 Formulas and Further Applications 8.5 Polynomial and Rational Inequalities Chapter 8 Summary Chapter 8 Review Exercises Chapter 8 Mixed Review Exercises Chapter 8 Test Chapters R–8 Cumulative Review Exercises Additional Graphs of Functions and Relations 9.1 Review of Operations and Composition 9.2 Graphs of Quadratic Functions 9.3 More About Parabolas and Their Applications 9.4 Symmetry; Increasing and Decreasing Functions 9.5 Piecewise Linear Functions Chapter 9 Summary Chapter 9 Review Exercises Chapter 9 Mixed Review Exercises Chapter 9 Test Chapters R–9 Cumulative Review Exercises Inverse, Exponential, and Logarithmic Functions 10.1 Inverse Functions 10.2 Exponential Functions 10.3 Logarithmic Functions 10.4 Properties of Logarithms 10.5 Common and Natural Logarithms 10.6 Exponential and Logarithmic Equations; Further Applications Chapter 10 Summary Chapter 10 Review Exercises Chapter 10 Mixed Review Exercises Chapter 10 Test Chapters R–10 Cumulative Review Exercises Polynomial and Rational Functions 11.1 Zeros of Polynomial Functions (I) 11.2 Zeros of Polynomial Functions (II) 11.3 Graphs and Applications of Polynomial Functions Summary Exercises: Examining Polynomial Functions and Graphs 11.4 Graphs and Applications of Rational Functions Chapter 11 Summary Chapter 11 Review Exercises Chapter 11 Mixed Review Exercises Chapter 11 Test Chapters R–11 Cumulative Review Exercises Conic Sections and Nonlinear Systems 12.1 Circles Revisited and Ellipses 12.2 Hyperbolas and Functions Defined by Radicals 12.3 Nonlinear Systems of Equations 12.4 Second-Degree Inequalities, Systems of Inequalities, and Linear Programming Chapter 12 Summary Chapter 12 Review Exercises Chapter 12 Mixed Review Exercises Chapter 12 Test Chapters R–12 Cumulative Review Exercises Further Topics in Algebra 13.1 Sequences and Series 13.2 Arithmetic Sequences 13.3 Geometric Sequences 13.4 The Binomial Theorem 13.5 Mathematical Induction 13.6 Counting Theory 13.7 Basics of Probability Chapter 13 Summary Chapter 13 Review Exercises Chapter 13 Mixed Review Exercises Chapter 13 Test Chapters R–13 Cumulative Review Exercises Appendix A: Solving Systems of Linear Equations by Matrix Methods Appendix B: Determinants and Cramer’s Rule Appendix C: Properties of Matrices Appendix D: Matrix Inverses Photo Credits Answers to Selected Exercises Index

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Book SynopsisMarge Lial (late) was always interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, was affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. Her interest in archeology led to trips to various digs and ruin sites, producing some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan. When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics education or journalism. His ultimate decision was to become a teacher, but afTable of ContentsTable of Contents Study Skill 1: Using Your Math Text Study Skill 2: Reading Your Math Text Study Skill 3: Taking Lecture Notes Study Skill 4: Completing Your Homework Study Skill 5: Using Study Cards Study Skill 6: Managing Your Time Study Skill 7: Reviewing a Chapter Study Skill 8: Taking Math Tests Study Skill 9: Analyzing Your Test Results Study Skill 10: Preparing for Your Math Final Review of the Real Number System R.1 Fractions, Decimals, and Percents R.2 Basic Concepts from Algebra R.3 Operations on Real Numbers R.3 Exponents, Roots, and Order of Operations R.4 Properties of Real Numbers Chapter R Summary Chapter R Test Linear Equations, Inequalities, and Applications 1.1 Linear Equations in One Variable 1.2 Formulas and Percent 1.3 Applications of Linear Equations 1.4 Further Applications of Linear Equations Summary Exercises: Applying Problem-Solving Techniques 1.5 Linear Inequalities in One Variable 1.6 Set Operations and Compound Inequalities 1.7 Absolute Value Equations and Inequalities Summary Exercises: Solving Linear and Absolute Value Equations and Inequalities Study Skills: Reviewing a Chapter Chapter 1 Summary Chapter 1 Review Exercises Chapter 1 Mixed Review Exercises Chapter 1 Test Chapters R and 1 Cumulative Review Exercises Linear Equations, Graphs, and Functions 2.1 Linear Equations in Two Variables 2.2 The Slope of a Line 2.3 Writing Equations of Lines Summary Exercises: Finding Slopes and Equations of Lines 2.4 Linear Inequalities in Two Variables 2.5 Introduction to Relations and Functions 2.6 Function Notation and Linear Functions Chapter 2 Summary Chapter 2 Review Exercises Chapter 2 Mixed Review Exercises Chapter 2 Test Chapters R—2 Cumulative Review Exercises Systems of Linear Equations 3.1 Systems of Linear Equations in Two Variables 3.2 Systems of Linear Equations in Three Variables 3.3 Applications of Systems of Linear Equations Chapter 3 Summary Chapter 3 Review Exercises Chapter 3 Mixed Review Exercises Chapter 3 Test Chapters R–3 Cumulative Review Exercises Exponents, Polynomials, and Polynomial Functions 4.1 Integer Exponents and Scientific Notation 4.2 Adding and Subtracting Polynomials 4.3 Polynomial Functions, Graphs, and Composition 4.4 Multiplying Polynomials 4.5 Dividing Polynomials Chapter 4 Summary Chapter 4 Review Exercises Chapter 4 Mixed Review Exercises Chapter 4 Test Chapters R–4 Cumulative Review Exercises Factoring 5.1 Greatest Common Factors and Factoring by Grouping 5.2 Factoring Trinomials 5.3 Special Factoring 5.4 A General Approach to Factoring 5.5 Solving Equations by the Zero-Factor Property Chapter 5 Summary Chapter 5 Review Exercises Chapter 5 Mixed Review Exercises Chapter 5 Test Chapters R–5 Cumulative Review Exercises Rational Expressions and Functions 6.1 Rational Expressions and Functions; Multiplying and Dividing 6.2 Adding and Subtracting Rational Expressions 6.3 Complex Fractions 6.4 Equations with Rational Expressions and Graphs Summary Exercises: Simplifying Rational Expressions vs. Solving Rational Equations 6.5 Applications of Rational Expressions 6.6 Variation Chapter 6 Summary Chapter 6 Review Exercises Chapter 6 Mixed Review Exercises Chapter 6 Test Chapters R–6 Cumulative Review Exercises Roots, Radicals, and Root Functions 7.1 Radical Expressions and Graphs 7.2 Rational Exponents 7.3 Simplifying Radicals, the Distance Formula, and Circles 7.4 Adding and Subtracting Radical Expressions 7.5 Multiplying and Dividing Radical Expressions Summary Exercises: Performing Operations with Radicals and Rational Exponents 7.6 Solving Equations with Radicals 7.7 Complex Numbers Chapter 7 Summary Chapter 7 Review Exercises Chapter 7 Mixed Review Exercises Chapter 7 Test Chapters R–7 Cumulative Review Exercises Quadratic Equations and Inequalities 8.1 The Square Root Property and Completing the Square 8.2 The Quadratic Formula 8.3 Equations That Lead to Quadratic Methods Summary Exercises: Applying Methods for Solving Quadratic Equations 8.4 Formulas and Further Applications 8.5 Polynomial and Rational Inequalities Chapter 8 Summary Chapter 8 Review Exercises Chapter 8 Mixed Review Exercises Chapter 8 Test Chapters R–8 Cumulative Review Exercises Additional Graphs of Functions and Relations 9.1 Review of Operations and Composition 9.2 Graphs of Quadratic Functions 9.3 More About Parabolas and Their Applications 9.4 Symmetry; Increasing and Decreasing Functions 9.5 Piecewise Linear Functions Chapter 9 Summary Chapter 9 Review Exercises Chapter 9 Mixed Review Exercises Chapter 9 Test Chapters R–9 Cumulative Review Exercises Inverse, Exponential, and Logarithmic Functions 10.1 Inverse Functions 10.2 Exponential Functions 10.3 Logarithmic Functions 10.4 Properties of Logarithms 10.5 Common and Natural Logarithms 10.6 Exponential and Logarithmic Equations; Further Applications Chapter 10 Summary Chapter 10 Review Exercises Chapter 10 Mixed Review Exercises Chapter 10 Test Chapters R–10 Cumulative Review Exercises Polynomial and Rational Functions 11.1 Zeros of Polynomial Functions (I) 11.2 Zeros of Polynomial Functions (II) 11.3 Graphs and Applications of Polynomial Functions Summary Exercises: Examining Polynomial Functions and Graphs 11.4 Graphs and Applications of Rational Functions Chapter 11 Summary Chapter 11 Review Exercises Chapter 11 Mixed Review Exercises Chapter 11 Test Chapters R–11 Cumulative Review Exercises Conic Sections and Nonlinear Systems 12.1 Circles Revisited and Ellipses 12.2 Hyperbolas and Functions Defined by Radicals 12.3 Nonlinear Systems of Equations 12.4 Second-Degree Inequalities, Systems of Inequalities, and Linear Programming Chapter 12 Summary Chapter 12 Review Exercises Chapter 12 Mixed Review Exercises Chapter 12 Test Chapters R–12 Cumulative Review Exercises Further Topics in Algebra 13.1 Sequences and Series 13.2 Arithmetic Sequences 13.3 Geometric Sequences 13.4 The Binomial Theorem 13.5 Mathematical Induction 13.6 Counting Theory 13.7 Basics of Probability Chapter 13 Summary Chapter 13 Review Exercises Chapter 13 Mixed Review Exercises Chapter 13 Test Chapters R–13 Cumulative Review Exercises Appendix A: Solving Systems of Linear Equations by Matrix Methods Appendix B: Determinants and Cramer’s Rule Appendix C: Properties of Matrices Appendix D: Matrix Inverses Photo Credits Answers to Selected Exercises Index

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Book SynopsisTable of ContentsTable of Contents Review R.1 Real Numbers R.2 Algebra Essentials R.3 Geometry Essentials R.4 Polynomials R.5 Factoring Polynomials R.6 Synthetic Division R.7 Rational Expressions R.8 nth Roots; Rational Exponents Equations and Inequalities 1.1 Linear Equations 1.2 Quadratic Equations 1.3 Complex Numbers; Quadratic Equations in the Complex Number System 1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations 1.5 Solving Inequalities 1.6 Equations and Inequalities Involving Absolute Value 1.7 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications Chapter 1 Review, Test, and Projects Graphs 2.1 The Distance and Midpoint Formulas 2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry 2.3 Lines 2.4 Circles 2.5 Variation Chapter 2 Review, Test, and Projects Functions and Their Graphs 3.1 Functions 3.2 The Graph of a Function 3.3 Properties of Functions 3.4 Library of Functions; Piecewise-defined Functions 3.5 Graphing Techniques: Transformations 3.6 Mathematical Models: Building Functions Chapter 3 Review, Test, and Projects Linear and Quadratic Functions 4.1 Properties of Linear Functions and Linear Models 4.2 Building Linear Models from Data 4.3 Quadratic Functions and Their Properties 4.4 Build Quadratic Models from Verbal Descriptions and from Data 4.5 Inequalities Involving Quadratic Functions Chapter 4 Review, Test, and Projects Polynomial and Rational Functions 5.1 Polynomial Functions 5.2 Graphing Polynomials Functions; Models 5.3 Properties of Rational Functions 5.4 The Graph of a Rational Function 5.5 Polynomial and Rational Inequalities 5.6 The Real Zeros of a Polynomial Function Chapter 5 Review, Test, and Projects Exponential and Logarithmic Functions 6.1 Composite Functions 6.2 One-to-One Functions; Inverse Functions 6.3 Exponential Functions 6.4 Logarithmic Functions 6.5 Properties of Logarithms 6.6 Logarithmic and Exponential Equations 6.7 Financial Models 6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models 6.9 Building Exponential, Logarithmic, and Logistic Models from Data Chapter 6 Review, Test, and Projects Trigonometric Functions 7.1 Angles, Arc, Length, and Circular Motion 7.2 Right Triangle Trigonometry 7.3 Computing the Values of Trigonometric Functions of Acute Angles 7.4 Trigonometric Functions of Any Angle 7.5 Unit Circle Approach; Properties of the Trigonometric Functions 7.6 Graphs of the Sine and Cosine Functions 7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions 7.8 Phase Shift; Sinusoidal Curve Fitting Chapter 7 Review, Test, and Projects Analytic Trigonometry 8.1 The Inverse Sine, Cosine, and Tangent Functions 8.2 The Inverse Trigonometric Functions (Continued) 8.3 Trigonometric Equations 8.4 Trigonometric Identities 8.5 Sum and Difference Formulas 8.6 Double-angle and Half-angle Formulas 8.7 Product-to-Sum and Sum-to-Product Formulas Chapter 8 Review, Test, and Projects Applications of Trigonometric Functions 9.1 Applications Involving Right Triangles 9.2 The Law of Sines 9.3 The Law of Cosines 9.4 Area of a Triangle 9.5 Simple Harmonic Motion; Damped Motion; Combining Waves Chapter 9 Review, Test, and Projects Polar Coordinates; Vectors 10.1 Polar Coordinates 10.2 Polar Equations and Graphs 10.3 The Complex Plane; De Moivre’s Theorem 10.4 Vectors 10.5 The Dot Product Chapter 10 Review, Test, and Projects Analytic Geometry 11.1 Conics 11.2 The Parabola 11.3 The Ellipse 11.4 The Hyperbola 11.5 Rotation of Axes; General Form of a Conic 11.6 Polar Equations of Conics 11.7 Plane Curves and Parametric Equations Chapter 11 Review, Test, and Projects Systems of Equations and Inequalities 12.1 Systems of Linear Equations: Substitution and Elimination 12.2 Systems of Linear Equations: Matrices 12.3 Systems of Linear Equations: Determinants 12.4 Matrix Algebra 12.5 Partial Fraction Decomposition 12.6 Systems of Nonlinear Equations 12.7 Systems of Inequalities 12.8 Linear Programming Chapter 12 Review, Test, and Projects Sequences; Induction; the Binomial Theorem 13.1 Sequences 13.2 Arithmetic Sequences 13.3 Geometric Sequences; Geometric Series 13.4 Mathematical Induction 13.5 The Binomial Theorem Chapter 13 Review, Test, and Projects Counting and Probability 14.1 Counting 14.2 Permutations and Combinations 14.3 Probability Chapter 14 Review, Test, and Projects Appendix: Graphing Utilities A.1 The Viewing Rectangle A.2 Using a Graphing Utility to Graph Equations A.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry A.4 Using a Graphing Utility to Solve Equations A.5 Square Screens A.6 Using a Graphing Utility to Graph Inequalities A.7 Using a Graphing Utility to Solve Systems of Linear Equations A.8 Using a Graphing Utility to Graph a Polar Equation A.9 Using a Graphing Utility to Graph Parametric Equations Answers Credits Index

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Book SynopsisThis concise introduction to the subject emphasizes the various classes of regular semigroups. More than 150 exercises, accompanied by references to the relevant research literature, direct readers to areas not explicitly covered in the text.Trade ReviewThe author succeeds admirably in his goal of providing an introduction to semigroup theory suitable for graduate students and non-specialists. At the same time, specialists will also find much to attract them. The book is highly readable, and the author takes pain to lead the reader gently through the longer proofs. I am sure that all specialists will want to own a copy of the book, that non-specialists will find it a most attractive and useful book for consulting, and that for many years to come research students will learn their subject from this book. * Bulletin of the London Mathematical Society *The book provides a useful survey of a rapidly developing topic and is suitable for specialists and as an introduction to the subject for non-specialists and graduate students. * Aslib Book Guide, vol.61, no.5, May 1996. *This book will still have its outstanding place as a general introduction to semigroup theory offering both an updated overview of the subject and a suitable entree for the graduate student * Monatshefte fur Mathematik Vol. 124 1997 *With this well-written and well-organised book I think the author has ensured that "Howie" will continue to be a byword for semigroup books * Edinburgh Mathematical Society 1997 *Table of Contents1. Introductory ideas ; 2. Green's equivalences; regular semigroups ; 3. 0-simple semigroups ; 4. Completely regular semigroups ; 5. Inverse semigroups ; 6. Other classes of regular semigroups ; 7. Free semigroups ; 8. Semigroup amalgams ; References ; List of symbols

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Book SynopsisThis is an introduction to the mathematical foundations of quantum field theory, using operator algebraic methods and emphasizing the link between the mathematical formulations and related physical concepts. It starts with a general probabilistic description of physics, which encompasses both classical and quantum physics. The basic key physical notions are clarified at this point. It then introduces operator algebraic methods for quantum theory, and goes on to discuss the theory of special relativity, scattering theory, and sector theory in this context.Trade Review'the self-contained monograph provides an introduction suitable for mathematics graduates to the basic properties of quantum fields' AslibTable of ContentsStates and observables ; Quantum theory ; The relativistic symmetry ; Local observables ; Scattering theory ; Sector theory ; Appendix A: Hilbert space and operators ; Appendix B: Operator algebras ; Appendix C: Free fields

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Book SynopsisAn accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles.Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie type.The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, a thorough treatment of Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields. Experts in the field will enjoy some of the new approaches to classical results.The text uses algebraic groups as the main examples, including worked out examples, instructive exercises, as well as bibliographical and historical remTrade Review'The author's intention was to write a quick introduction to the area of algebraic groups of the Lie type over fields of positive characteristic and I think he was very successful. The first part of the book can be recommended as a very suitable text for undergraduate students at the beginning of their studies.' * EMS Newsletter *The style of exposition in the book is very reader-friendly ... The proofs are clear and complete. * Mathematical Reviews *Table of Contents1. Algebraic sets and algebraic groups ; 2. Affine varieties and finite morphisms ; 3. Algebraic representations and Borel subgroups ; 4. Frobenius maps and finite groups of Lie type ; Bibliography ; Index

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Book SynopsisPresents easy to understand proofs of some of the most difficult results about polynomials demonstrated by means of applications.Trade ReviewPresents easy to understand proofs of some of the most difficult results about polynomials demonstrated by means of applications ... Brings to the subject an immense range of reference to the study of polynomials. Professional and academic mathematicians of complex analysis, approximation theory and theoretical numerical analysis; graduate students in mathematics; engineers, statisticians and theoretical physicists, who have an interest in the important results about polynomials, will not do better than start with reading and referring to this book. * Current Engineering Practice *A nicely written book that will be useful for scientists, engineers and mathematicians from other fields. It can be strongly recommended as an undergraduate or graduate text and as a comprehensive source for self study. * EMS *Table of Contents2. FUNDAMENTAL RESULTS ON CRITICAL POINTS ; 8. INCLUSION OF ALL ZEROS ; 12. GROWTH ESTIMATES

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Book SynopsisThis work summarises the development of a classification system of finite p-groups. The authors provide a careful summary and explanation of the many and difficult original research papers on the co-class conjecture and the structure theorem, thus elucidating the background research for those new to the area as well as for experienced researchers.Trade Review... there is considerable new material in this book ... The book is beautifully produced - a pleasure to the eyes, as well as to the mind, to read. * Zentralblatt MATH *Table of Contents1. Preliminaries ; 2. New groups from old ; 3. p-groups of maximal class ; 4. Finite p-groups acting uniserially ; 5. Lie Methods ; 6. The proof of Conjecture A ; 7. Pro-p-groups ; 8. Constructing finite p-groups ; 9. Homological algebra ; 10. Uniserial p-adic space groups ; 11. The structure of finite p-groups ; 12. Beyond coclass ; Bibliography ; Symbol index ; index

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Book SynopsisLoop groups are the simplest class of infinite dimensional Lie groups, and have important applications in elementary particle physics. They have recently been studied intensively, and the theory is now well developed, involving ideas from several areas of mathematics - algebra, geometry, analysis, and combinatorics. The mathematics of quantum field theory is an important ingredient. This book gives a complete and self-contained account of what is known about the subject and it is written from a geometrical and analytical point of view, with quantum field theory very much in mind. The mathematics used in connection with loop groups is interesting and important beyond its immediate applications and the authors have tried to make the book accessible to mathematicians in many fields.The hardback edition was published in December 1986.Trade Review'This is an outstanding book, of enormous interest to anyone interested in Lie groups, Lie algebras and/or Quantum Field Theory' MathematikaTable of ContentsIntroduction; PART 1 - Finite dimensional lie groups; Groups of smooth maps; Central extensions; The root system: KAC-Moody algebras; Loop groups as groups of operators in Hilbert space; The Grassmannian of Hilbert space and the determinant line bundle; The fundamental homogeneous space. PART 2 - Representation theory; The fundamental representation; The Borel-Weil theory; The spin representation; 'Blips' or 'vertex operators'; The KAC character formula and the Bernstein-Gelfand-Gelfand resolution; References; Index of notation; Index.

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Book SynopsisThis monograph provides a treatment of the theory of algebraic Riccati equations, an area of increasing interest in the mathematics and engineering communities. A range of applications are covered, demonstrating the use of these equations for providing solutions to complex problems.Table of Contents1. Preliminaries from the theory of matrices ; 2. Indefinite scalar products ; 3. Skew-symmetric scalar products ; 4. Matrix theory and control ; 5. Linear matrix equations ; 6. Rational matrix functions ; 7. Geometric theory: the complex case ; 8. Geometric theory: the real case ; 9. Constructive existence and comparison theorems ; 10. Hermitian solutions and factorizations of rational matrix functions ; 11. Perturbation theory ; 12. Geometric theory for the discrete algebraic Riccati equation ; 13. Constructive existence and comparison theorems ; 14. Perturbation theory for discrete algebraic Riccati equations ; 15. Discrete algebraic Riccati equations and matrix pencils ; 16. Linear-quadratic regulator problems ; 17. The discrete Kalman filter ; 18. The total least squares technique ; 19. Canonical factorization ; 20. Hoo control problems ; 21. Contractive rational matrix functions ; 22. The matrix sign function ; 23. Structured stability radius ; Bibliography ; List of notations ; Index

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Book SynopsisHeun''s equation is a second-order differential equation which crops up in a variety of forms in a wide range of problems in applied mathematics. These include integral equations of potential theory, wave propogation, electrostatic oscillation, and Schrodinger''s equation. This volume brings together important research work for the first time, providing an important resource for all those interested in this mathematical topic. Both the current theory and the main areas of application are surveyed, and includes contributions from authoritative researchers such as Felix Arscott (Canada), P. Maroni (France), and Gerhard Wolf (Germany).Trade ReviewThere is a wealth of important results and open problems and the book is a welcome addition to the literature on these important special functions and their applications. * B D Sleeman, Zbl. Math. 847/96. *Table of ContentsA. HEUN'S EQUATION ; I: GENERAL AND POWER SERIES ; II: HYPERGEOMETRIC FUNCTION SERIES ; B. CONFLUENT HEUN EQUATION ; C. DOUBLE CONFLUENT HEUN EQUATION ; D. BICONFLUENT HEUN EQUATION ; E. TRICONFLUENT HEUN EQUATION

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Book SynopsisThis textbook provides a modern introduction to linear algebra, a mathematical discipline every first year undergraduate student in physics and engineering must learn. A rigorous introduction into the mathematics is combined with many examples, solved problems, and exercises as well as scientific applications of linear algebra. These include applications to contemporary topics such as internet search, artificial intelligence, neural networks, and quantum computing, as well as a number of more advanced topics, such as Jordan normal form, singular value decomposition, and tensors, which will make it a useful reference for a more experienced practitioner. Structured into 27 chapters, it is designed as a basis for a lecture course and combines a rigorous mathematical development of the subject with a range of concisely presented scientific applications. The main text contains many examples and solved problems to help the reader develop a working knowledge of the subject and every chapter comes with exercises.Trade ReviewThe authors are uniquely well qualified to produce a textbook suitable for first-year university students. * David Matravers, University of Portsmouth *Linear Algebra is a core undergraduate course not only in Mathematics but also in Physics, Chemistry, Biology and Computer Science. This textbook brilliantly succeeds in catering to such a wide audience by covering a broad range of formal developments along with concrete applications and is unique in its presentation of the topic. * Richard Joseph Szabo, Heriot-Watt University *Lukas has written an impressive mathematical textbook that covers standard introductory linear algebra topics along with advanced concepts that will appeal to many readers. * Choice *Table of Contents1: Linearity - an informal introduction 2: Sets and functions 3: Groups 4: Fields 5: Coordinate vectors 6: Vector spaces 7: Elementary vector space properties 8: Vector subspaces 9: The dot product 10: Vector and triple product 11: Lines and planes 12: Introduction to linear maps 13: Matrices 14: The structure of linear maps 15: Linear maps in terms of matrices 16: Computing with matrices 17: Linear systems 18: Determinants 19: Basics of eigenvalues 20: Diagonalising linear maps 21: The Jordan normal form 22: Scalar products 23: Adjoint and unitary maps 24: Diagonalisation - again 25: Bi-linear and sesqui-linear forms 26: The dual vector space 27: Tensors

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Book SynopsisHow fast can you calculate? Would you like to be faster? This book presents the time honored tricks and tips of calculation, from a fresh perspective, to boost the speed at which you can add whether a couple of numbers, or columns so long an accountant may faint. Find out how to subtract, multiply, divide, and find square roots more quickly.Trade ReviewIf you think mental arithmetic is out of date in the 21st century, think again. This engaging book is about insight and interestingness beyond the simple utility of quicker calculations. The general style is original and characterful, and makes the book distinctive. * Prasenjit Saha, University of Zurich *This book is about very elementary concepts that ought to be read by sophisticated people who appreciate that elementary does not mean trivial. The author's erudite scholarship shines in the prose, along with just the right level of dry wit. It's serious stuff he's writing about (without numbers and arithmetic, our modern world simply vanishes into the ancient past where numbers were limited to none, one, and many), but in such a way that the reader does not slowly nod-off into a coma. * Paul J. Nahin, University of New Hampshire *Lipscombe's book is unusual, being, as it is, an expansive view of a small subject. The text he presents here is excellent, and is a model of everything a writer strives for: concision, simplicity, directness, accuracy, and surprise. * Don S. Lemons, Bethel College, Kansas *Table of ContentsPreface Introduction Challenge 1: Arithmetical Advice 2: Speedier Sums and Subtractions Interlude I: The Magic of 111,111 3: Accounting for Taste -- Adding Columns Quickly Interlude II: Checking, Check Digits, and Casting out Nines 4: Quicker Quotients and Pleasing Products -- Multiply and Divide by Specific Numbers Interlude III: Doomsday 5: Calculations with Constraints -- Multiply and Divide by Numbers with Specific Properties Interlude IV: Multicultural Multiplication 6: Super Powers -- Calculate Squares, Square Roots, Cube Roots, and More 7: Close-Enough Calculations -- Quick and Accurate Approximations Interlude V: Approximating the Number of Space Aliens 8: Multiplying Irrationally The Grand Finale Further Reading Appendix I: Calculating Doomsday Appendix II: The Squares from 1 to 100

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Book SynopsisLie Groups is intended as an introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. It covers the essentials of the subject starting from basic undergraduate mathematics. The correspondence between linear Lie groups and Lie algebras is developed in its local and global aspects. The classical groups are analysed in detail, first with elementary matrix methods, then with the help of the structural tools typical of the theory of semisimple groups, such as Cartan subgroups, roots, weights, and reflections. The fundamental groups of the classical groups are worked out as an application of these methods. Manifolds are introduced when needed, in connection with homogeneous spaces, and the elements of differential and integral calculus on manifolds are presented, with special emphasis on integration on groups and homogeneous spaces. Representation theory starts from first principles, such as Schur''s lemma and its consequenTrade Review'A nice feature of this book is a variety of problems proposed at the end of each section; this makes it especially suitable as a textbook for a first course in Lie groups, addressed to an audience of mathematicians or physicists. MMA Reviews, March 2007, Fabio MainardiTable of ContentsPreface ; 1. The exponential map ; 2. Lie theory ; 3. The classical groups ; 4. Manifolds, homogeneous spaces, Lie groups ; 5. Integration ; 6. Representations ; Appendix: Analytic Functions and Inverse Function Theorem ; References ; Index

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Book SynopsisBanach spaces and algebras are a key topic of pure mathematics. Graham Allan''s careful and detailed introductory account will prove essential reading for anyone wishing to specialise in functional analysis and is aimed at final year undergraduates or masters level students. Based on the author''s lectures to fourth year students at Cambridge University, the book assumes knowledge typical of first degrees in mathematics, including metric spaces, analytic topology, and complex analysis. However, readers are not expected to be familiar with the Lebesgue theory of measure and integration.The text begins by giving the basic theory of Banach spaces, including dual spaces and bounded linear operators. It establishes forms of the theorems that are the pillars of functional analysis, including the Banach-Alaoglu, Hahn-Banach, uniform boundedness, open mapping, and closed graph theorems. There are applications to Fourier series and operators on Hilbert spaces.The main body of the text is an intTrade ReviewThis well-crafted and scholarly book ...leaves nothing to be desired: this is a fine way to get into this beautiful in a subject and will serve to reel in a huge number of futureews devotees. * Michael Berg, MAA Reviews *Table of ContentsPART I INTRODUCTION TO BANACH SPACES ; 1. Preliminaries ; 2. Elements of normed spaces ; 3. Banach spaces ; PART II BANACH ALGEBRAS ; 4. Banach algebras ; 5. Representation theory ; 6. Algebras with an involution ; 7. The Borel functional calculus ; PART III SCV AND BANACH ALGEBRAS ; 8. Introduction to several complex variables ; 9. The holomorphic functional calculus in several variables ; Bibliography ; Index

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Book SynopsisAn Introduction to the Theory of Numbers by G.H. Hardy and E. M. Wright is found on the reading list of virtually all elementary number theory courses and is widely regarded as the primary and classic text in elementary number theory. Developed under the guidance of D.R. Heath-Brown this Sixth Edition of An Introduction to the Theory of Numbers has been extensively revised and updated to guide today''s students through the key milestones and developments in number theory. Updates include a chapter by J.H. Silverman on one of the most important developments in number theory -- modular elliptic curves and their role in the proof of Fermat''s Last Theorem -- a foreword by A. Wiles, and comprehensively updated end-of-chapter notes detailing the key developments in number theory. Suggestions for further reading are also included for the more avid readerThe text retains the style and clarity of previous editions making it highly suitable for undergraduates in mathematics from the first year Trade ReviewReview from previous edition Mathematicians of all kinds will find the book pleasant and stimulating reading, and even experts on the theory of numbers will find that the authors have something new to say on many of the topics they have selected... Each chapter is a model of clear exposition, and the notes at the ends of the chapters, with the references and suggestions for further reading, are invaluable. * Nature *This fascinating book... gives a full, vivid and exciting account of its subject, as far as this can be done without using too much advanced theory. * Mathematical Gazette *...an important reference work... which is certain to continue its long and successful life... * Mathematical Reviews *...remains invaluable as a first course on the subject, and as a source of food for thought for anyone wishing to strike out on his own. * Matyc Journal *Table of ContentsPREFACE TO THE SIXTH EDITION; PREFACE TO THE FIFTH EDITION; APPENDIX; LIST OF BOOKS; INDEX OF SPECIAL SYMBOLS AND WORDS; INDEX OF NAMES; GENERAL INDEX

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Book SynopsisAdvanced Topics in Linear Algebra presents, in an engaging style, novel topics linked through the Weyr matrix canonical form, a largely unknown cousin of the Jordan canonical form discovered by Eduard Weyr in 1885. The book also develops much linear algebra unconnected to canonical forms, that has not previously appeared in book form. It presents common applications of Weyr form, including matrix commutativity problems, approximate simultaneous diagonalization, and algebraic geometry, with the latter two having topical connections to phylogenetic invariants in biomathematics and multivariate interpolation. The Weyr form clearly outperforms the Jordan form in many situations, particularly where two or more commuting matrices are involved, due to the block upper triangular form a Weyr matrix forces on any commuting matrix. In this book, the authors develop the Weyr form from scratch, and include an algorithm for computing it. The Weyr form is also derived ring-theoretically in an entirely different way to the classical derivation of the Jordan form. A fascinating duality exists between the two forms that allows one to flip back and forth and exploit the combined powers of each. The book weaves together ideas from various mathematical disciplines, demonstrating dramatically the variety and unity of mathematics. Though the book''s main focus is linear algebra, it also draws upon ideas from commutative and noncommutative ring theory, module theory, field theory, topology, and algebraic geometry.Advanced Topics in Linear Algebra offers self-contained accounts of the non-trivial results used from outside linear algebra, and lots of worked examples, thereby making it accessible to graduate students. Indeed, the scope of the book makes it an appealing graduate text, either as a reference or for an appropriately designed one or two semester course. A number of the authors'' previously unpublished results appear as well.Trade Review"The book covers both early and quite recent results, has informative remarks and thorough theoretical deductions, provides interesting footnotes and brief biographies of related mathematicians, and contains concrete and elegant proofs. Overall, the book is written in a self-contained, introductory, and inspiring fashion." Mathematical ReviewsTable of ContentsPreface ; Chapter 1. Background Linear Algebra ; Chapter 2. The Weyr Form ; Chapter 3. Centralizers ; Chapter 4. The Module Setting ; Chapter 5. Gerstenhaber's Theorem ; Chapter 6. Approximate Simultaneous Diagonalization ; Chapter 7. Algebraic Varieties ; Bibliography

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Book SynopsisConsidered a classic by many, A First Course in Abstract Algebra is an in-depth introduction to abstract algebra. Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures.Table of Contents(*) Not required for the remainder of the text. (**) This section is required only for Chapters 17 and 36.). 0. Sets and Relations. I. GROUPS AND SUBGROUPS. 1. Introduction and Examples. 2. Binary Operations. 3. Isomorphic Binary Structures. 4. Groups. 5. Subgroups. 6. Cyclic Groups. 7. Generators and Cayley Digraphs. II. PERMUTATIONS, COSETS, AND DIRECT PRODUCTS. 8. Groups of Permutations. 9. Orbits, Cycles, and the Alternating Groups. 10. Cosets and the Theorem of Lagrange. 11. Direct Products and Finitely Generated Abelian Groups. 12. *Plane Isometries. III. HOMOMORPHISMS AND FACTOR GROUPS. 13. Homomorphisms. 14. Factor Groups. 15. Factor-Group Computations and Simple Groups. 16. **Group Action on a Set. 17. *Applications of G-Sets to Counting. IV. RINGS AND FIELDS. 18. Rings and Fields. 19. Integral Domains. 20. Fermat's and Euler's Theorems. 21. The Field of Quotients of an Integral Domain. 22. Rings of Polynomials. 23. Factorization of Polynomials over a Field. 24. *Noncommutative Examples. 25. *Ordered Rings and Fields. V. IDEALS AND FACTOR RINGS. 26. Homomorphisms and Factor Rings. 27. Prime and Maximal Ideas. 28. *Gröbner Bases for Ideals. VI. EXTENSION FIELDS. 29. Introduction to Extension Fields. 30. Vector Spaces. 31. Algebraic Extensions. 32. *Geometric Constructions. 33. Finite Fields. VII. ADVANCED GROUP THEORY. 34. Isomorphism Theorems. 35. Series of Groups. 36. Sylow Theorems. 37. Applications of the Sylow Theory. 38. Free Abelian Groups. 39. Free Groups. 40. Group Presentations. VIII. *GROUPS IN TOPOLOGY. 41. Simplicial Complexes and Homology Groups. 42. Computations of Homology Groups. 43. More Homology Computations and Applications. 44. Homological Algebra. IX. Factorization. 45. Unique Factorization Domains. 46. Euclidean Domains. 47. Gaussian Integers and Multiplicative Norms. X. AUTOMORPHISMS AND GALOIS THEORY. 48. Automorphisms of Fields. 49. The Isomorphism Extension Theorem. 50. Splitting Fields. 51. Separable Extensions. 52. *Totally Inseparable Extensions. 53. Galois Theory. 54. Illustrations of Galois Theory. 55. Cyclotomic Extensions. 56. Insolvability of the Quintic. Appendix: Matrix Algebra. Notations. Answers to odd-numbered exercises not asking for definitions or proofs. Index.

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Book SynopsisIn this book, I. Ya. Bakel'man introduces inversion transformations in the Euclidean plane and discusses the interrelationships among more general mathematical concepts. The author begins by defining and giving examples of the concept of a transformation in the Euclidean plane, and then explains the point of infinity and the stereographic projection of the sphere onto the plane. With this preparation, the student is capable of applying the theory of inversions to classical construction problems in the plane. The author also discusses the theory of pencils of circles, and he uses the acquired techniques in a proof of Ptolemy's theorem. In the final chapter, the idea of a group is introduced with applications of group theory to geometry. The author demonstrates the group-theoretic basis for the distinction between Euclidean and Lobachevskian geometry.

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Book SynopsisExplores the role of group actions and rigidity in several areas of mathematics, including ergodic theory, dynamics, geometry, topology, and the algebraic properties of representation varieties.

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Book SynopsisMark Dugopolski was born in Menominee, Michigan. After receiving a BS from Michigan State University, he taught high school in Illinois for four years. He received an MS in mathematics from Northern Illinois University at DeKalb. He then received a PhD in the area of topology and an MS in statistics from the University of Illinois at ChampaignUrbana. Mark taught mathematics at Southeastern Louisiana University in Hammond for twenty-five years and now holds the rank of Professor Emeritus of Mathematics. He has been writing textbooks since 1988. He is married and has two daughters. In his spare time he enjoys tennis, jogging, bicycling, fishing, kayaking, gardening, bridge, and motorcycling.Table of ContentsP. Prerequisites P.1 Real Numbers and Their Properties P.2 Integral Exponents and Scientific Notation P.3 Rational Exponents and Radicals P.4 Polynomials P.5 Factoring Polynomials P.6 Rational Expressions P.7 Complex Numbers 1. Equations, Inequalities, and Modeling 1.1 Linear, Rational, and Absolute Value Equations 1.2 Constructing Models to Solve Problems 1.3 Equations and Graphs in Two Variables 1.4 Linear Equations in Two Variables 1.5 Quadratic Equations 1.6 Miscellaneous Equations 1.7 Linear and Absolute Value Inequalities 2. Functions and Graphs 2.1 Functions 2.2 Graphs of Relations and Functions 2.3 Families of Functions, Transformations, and Symmetry 2.4 Operations with Functions 2.5 Inverse Functions 2.6 Constructing Functions with Variation 3. Polynomial and Rational Functions 3.1 Quadratic Functions and Inequalities 3.2 Zeros of Polynomial Functions 3.3 The Theory of Equations 3.4 Graphs of Polynomial Functions 3.5 Rational Functions and Inequalities 4. Exponential and Logarithmic Functions 4.1 Exponential Functions and Their Applications 4.2 Logarithmic Functions and Their Applications 4.3 Rules of Logarithms 4.4 More Equations and Applications 5. The Trigonometric Functions 5.1 Angles and Their Measurements 5.2 The Sine and Cosine Functions 5.3 The Graphs of the Sine and Cosine Functions 5.4 The Other Trigonometric Functions and Their Graphs 5.5 The Inverse Trigonometric Functions 5.6 Right Triangle Trigonometry 6. Trigonometric Identities and Conditional Equations 6.1 Basic Identities 6.2 Verifying Identities 6.3 Sum and Difference Identities 6.4 Double-Angle and Half-Angle Identities 6.5 Product and Sum Identities 6.6 Conditional Trigonometric Equations 7. Applications of Trigonometry 7.1 The Law of Sines 7.2 The Law of Cosines 7.3 Vectors 7.4 Trigonometric Form of Complex Numbers 7.5 Powers and Roots of Complex Numbers 7.6 Polar Equations 7.7 Parametric Equations 8. Systems of Equations and Inequalities 8.1 Systems of Linear Equations in Two Variables 8.2 Systems of Linear Equations in Three Variables 8.3 Nonlinear Systems of Equations 8.4 Partial Fractions 8.5 Inequalities and Systems of Inequalities in Two Variables 8.6 The Linear Programming Model 9. Matrices and Determinants 9.1 Solving Linear Systems Using Matrices 9.2 Operations with Matrices 9.3 Multiplication of Matrices 9.4 Inverses of Matrices 9.5 Solution of Linear Systems in Two Variables Using Determinants 9.6 Solution of Linear Systems in Three Variables Using Determinants 10. The Conic Sections 10.1 The Parabola 10.2 The Ellipse and the Circle 10.3 The Hyperbola 11. Sequences, Series, and Probability 11.1 Sequences and Arithmetic Sequences 11.2 Series and Arithmetic Series 11.3 Geometric Sequences and Series 11.4 Counting and Permutations 11.5 Combinations, Labeling, and the Binomial Theorem 11.6 Probability 11.7 Mathematical Induction

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Book SynopsisThis manual provides detailed solutions to odd-numbered exercises in the text.

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Book SynopsisTable of ContentsIndex of Applications Preface 1. Whole Numbers 1.1 Standard Notation 1.2 Addition 1.3 Subtraction 1.4 Multiplication 1.5 Division Mid-Chapter Review 1.6 Rounding and Estimating; Order 1.7 Solving Equations 1.8 Applications and Problem Solving Translating for Success 1.9 Exponential Notation and Order of Operations Summary and Review Test 2. Fraction Notation: Multiplication and Division 2.1 Factorizations 2.2 Divisibility 2.3 Fractions and Fraction Notation 2.4 Multiplication and Applications 2.5 Simplifying Mid-Chapter Review 2.6 Multiplying, Simplifying, and Applications 2.7 Division and Applications Translating for Success Summary and Review Test 3. Fraction Notation and Mixed Numerals 3.1 Least Common Multiples 3.2 Addition and Applications 3.3 Subtraction, Order, and Applications Translating for Success 3.4 Mixed Numerals Mid-Chapter Review 3.5 Addition and Subtraction Using Mixed Numerals; Applications 3.6 Multiplication and Division Using Mixed Numerals; Applications Translating for Success 3.7 Order of Operations, Complex Fractions, and Estimation Summary and Review Test Cumulative Review 4. Decimal Notation 4.1 Decimal Notation, Order, and Rounding 4.2 Addition and Subtraction 4.3 Multiplication 4.4 Division Mid-Chapter Review 4.5 Converting from Fraction Notation to Decimal Notation 4.6 Estimating 4.7 Applications and Problem Solving Translating for Success Summary and Review Test Cumulative Review 5. Ratio and Proportion 5.1 Introduction to Ratios 5.2 Rates and Unit Prices 5.3 Proportions Mid-Chapter Review 5.4 Applications of Proportions Translating for Success 5.5 Geometric Applications Summary and Review Test Cumulative Review 6. Percent Notation 6.1 Percent Notation 6.2 Percent Notation and Fraction Notation 6.3 Solving Percent Problems Using Percent Equations 6.4 Solving Percent Problems Using Proportions Mid-Chapter Review 6.5 Applications of Percent Translating for Success 6.6 Sales Tax, Commission, and Discount 6.7 Simple Interest and Compound Interest; Credit Cards Summary and Review Test Cumulative Review 7. Data, Graphs, and Statistics 7.1 Averages, Medians, and Modes 7.2 Interpreting Data from Tables and Graphs Mid-Chapter Review 7.3 Interpreting and Drawing Bar Graphs and Line Graphs 7.4 Interpreting and Drawing Circle Graphs Translating for Success Summary and Review Test Cumulative Review 8. Measurement 8.1 Linear Measures: American Units 8.2 Linear Measures: The Metric System 8.3 Converting Between American Units and Metric Units Mid-Chapter Review 8.4 Weight and Mass; Medical Applications 8.5 Capacity; Medical Applications 8.6 Time and Temperature 8.7 Converting Units of Area Translating for Success Summary and Review Test Cumulative Review 9. Geometry 9.1 Perimeter 9.2 Area 9.3 Circles Mid-Chapter Review 9.4 Volume 9.5 Angles and Triangles 9.6 Square Roots and the Pythagorean Theorem Translating for Success Summary and Review Test Cumulative Review 10. Real Numbers 10.1 The Real Numbers 10.2 Addition of Real Numbers 10.3 Subtraction of Real Numbers Mid-Chapter Review 10.4 Multiplication of Real Numbers 10.5 Division of Real Numbers and Order of Operations Translating for Success Summary and Review Test Cumulative Review 11. Algebra: Solving Equations and Problems 11.1 Introduction to Algebra 11.2 Solving Equations: The Addition Principle 11.3 Solving Equations: The Multiplication Principle Mid-Chapter Review 11.4 Using the Principles Together 11.5 Applications and Problem Solving Translating for Success Summary and Review Test Cumulative Review Answers Guided Solutions Glossary Index

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